Factor Vocab Word 2 Its meaning (As it is used Scientists are - - PDF document

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Scientific Notation

8th Grade

www.njctl.org 2014-10-27

Slide 3 / 127 Table of Contents

· The purpose of scientific notation · How to write numbers in scientific notation · How to convert between scientific notation 
 and standard form · Multiply and Divide with scientific notation · Comparing numbers in scientific notation

Click on the topic to go to that section

· Addition and Subtraction with scientific notation · Glossary · Magnitude

Slide 4 / 127

Sometimes when you subtract the fractions, you find that you can't because the first numerator is smaller than the second! When this happens, you need to regroup from the whole number. How many thirds are in 1 whole? How many fifths are in 1 whole? How many ninths are in 1 whole?

Vocabulary words are identified with a dotted underline.

The underline is linked to the glossary at the end of the

• Notebook. It can also be printed for a word wall.

(Click on the dotted underline.)

Slide 5 / 127

Back to Instruction

Factor

A whole number that can divide into another number with no remainder.

15 3 5

3 is a factor of 15

3 x 5 = 15

3 and 5 are factors of 15

16 3 5 .1

R 3 is not a factor of 16

A whole number that multiplies with another number to make a third number.

The charts have 4 parts.

Vocab Word

1

Its meaning

2

Examples/ Counterexamples

3

Link to return to the instructional page.

4

(As it is used in the lesson.)

Slide 6 / 127

Scientists are often confronted with numbers that look like this: 300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000 kg Can you guess what weighs this much?

Purpose of Scientific Notation

Return to Table of Contents

Slide 7 / 127

Blue Whale - largest animal on earth The Great Pyramid at Giza Total Human Population The Earth

The Sun

2,000,000,000,000,000, 000,000,000,000,000 kg 60,000,000,000,000, 000,000,000,000 kg 300,000,000,000 kg 600,000,000 kg 180,000 kg

Can you match these BIG objects to their weights?

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60,000,000,000,000, 000,000,000,000 kg 2,000,000,000,000,000, 000,000,000,000,000 kg 300,000,000,000 kg 600,000,000 kg 180,000 kg

Blue Whale - largest animal on earth The Great Pyramid at Giza Total Human Population The Earth

The Sun

Can you match these BIG objects to their weights?

Click object to reveal answer

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0.00000000035 kg 0.00015 kg 0.000000000000000000000000030 kg

Can you match these small

• bjects to their weights?

grain of sand molecule steam

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0.00000000035 kg 0.00015 kg

Click to reveal answers.

0.000000000000000000000000030 kg grain of sand molecule steam

Slide 11 / 127

The examples were written in "standard form", the form we normally use. But the standard form is difficult to work with when a number is HUGE or tiny, if it has a lot of zeros. Scientists have come up with a more convenient method to write very LARGE and very small numbers.

Scientific Notation

Writing numbers in scientific notation doesn't change the value of the number.

Slide 12 / 127

Scientific Notation uses Powers of 10 to write big or small numbers more conveniently. Using scientific notation requires us to use the rules of exponents we learned earlier. While we developed those rules for all bases, scientific notation only uses base 10.

Scientific Notation

Slide 13 / 127 Powers of Ten

click here to see a video on powers of ten which puts our universe into perspective!

101 = 10 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1,000 104 = 10 x 10 x 10 x 10 = 10,000 105 = 10 x 10 x 10 x 10 x 10 = 100,000

click here to move from the Milky Way through space towards Earth to a oak tree, and then within a cell !

Slide 14 / 127 Powers of Integers

Powers are a quick way to write repeated multiplication, just as multiplication was a quick way to write repeated addition. These are all equivalent: 103 (10)(10)(10) 1000 In this case, the base is 10 and the exponent is 3.

Slide 15 / 127

Remember that when multiplying numbers with exponents, if the bases are the same, you write the base and add the exponents. 2

5 x 2 6 = 2 (5+6) = 2 11

33 x 3

7 = 3

(3+7) = 3

10

10

8 x 10

• 3 = 10

(8+-3)

= 10

5

47 x 4

• 7 = 4

(7+-7) = 4 0 = 1

Exponent Rules Slide 16 / 127

1 102 x 104 =

A 106 B 108 C 1010 D 1012

Answer

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1 102 x 104 =

A 106 B 108 C 1010 D 1012

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Answer A

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2 1014 x 10-6 =

A 106 B 108 C 1010 D 1012

Answer

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2 1014 x 10-6 =

A 106 B 108 C 1010 D 1012

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Answer B

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3 10-4 x 10-6 =

A 10-6 B 10-8 C 10-10 D 10-12

Answer

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3 10-4 x 10-6 =

A 10-6 B 10-8 C 10-10 D 10-12

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Answer C

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4 104 x 106 =

A 106 B 108 C 1010 D 1012

Answer

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4 104 x 106 =

A 106 B 108 C 1010 D 1012

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Answer C

Slide 20 / 127 Writing Numbers in Scientific Notation

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Slide 21 / 127 Writing Large Numbers in Scientific Notation Slide 22 / 127

Here are some different ways of writing 6,500. 6,500 = 6.5 thousand 6.5 thousand = 6.5 x 1,000 6.5 x 1,000 = 6.5 x 10

3

which means that 6,500 = 6.5 x 103 6,500 is standard form of the number and 6.5 x 10

3 is scientific

notation These are two ways of writing the same number.

Scientific Notation Slide 23 / 127

6.5 x 10

3 isn't a lot more convenient than 6,500.

But let's do the same thing with 7,400,000,000 which is equal to 7.4 billion which is 7.4 x 1,000,000,000 which is 7.4 x 10

9

Besides being shorter than 7,400,000,000 it is a lot easier to keep track

• f the zeros in scientific notation.

And we'll see that the math gets a lot easier as well.

Scientific Notation Slide 24 / 127

Scientific notation expresses numbers as the product of: a coefficient and 10 raised to some power . 3.78 x 10

6

The coefficient is always greater than or equal to one, and less than 10. In this case, the number 3,780,000 is expressed in scientific notation.

Scientific Notation Slide 25 / 127 Express 870,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit.

870000 870000 x 10

.

870000 x 10

.

1 2 3 4 5

8.7 x 105

Slide 26 / 127 Express 53,600 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit. Answer

Slide 26 (Answer) / 127 Express 53,600 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit.

[This object is a pull tab]

Answer 5.36 x 10

4

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Express 284,000,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit. Answer

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Express 284,000,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit.

[This object is a pull tab]

Answer 2.84 x 10

8

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5 Which is the correct coefficient of 147,000 when it is written in scientific notation? A 147 B 14.7 C 1.47 D .147

Answer

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5 Which is the correct coefficient of 147,000 when it is written in scientific notation? A 147 B 14.7 C 1.47 D .147

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Answer C

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6 Which is the correct coefficient of 23,400,000 when it is written in scientific notation? A .234 B 2.34 C 234. D 23.4

Answer

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6 Which is the correct coefficient of 23,400,000 when it is written in scientific notation? A .234 B 2.34 C 234. D 23.4

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Answer B

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7 How many places do you need to move the decimal point to change 190,000 to 1.9? A 3 B 4 C 5 D 6

Answer

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7 How many places do you need to move the decimal point to change 190,000 to 1.9? A 3 B 4 C 5 D 6

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Answer C

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8 How many places do you need to move the decimal point to change 765,200,000,000 to 7.652? A 11 B 10 C 9 D 8

Answer

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8 How many places do you need to move the decimal point to change 765,200,000,000 to 7.652? A 11 B 10 C 9 D 8

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Answer A

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9 Which of the following is 345,000,000 in scientific notation? A 3.45 x 108 B 3.45 x 106 C 345 x 106 D .345 x 109

Answer

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9 Which of the following is 345,000,000 in scientific notation? A 3.45 x 108 B 3.45 x 106 C 345 x 106 D .345 x 109

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Answer A

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10 Which of these is not a number greater than one in scientific notation? A .34 x 108 B 7.2 x 103 C 8.9 x 104 D 2.2 x 10-1 E 11.4 x 1012 F .41 x 103

Answer

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10 Which of these is not a number greater than one in scientific notation? A .34 x 108 B 7.2 x 103 C 8.9 x 104 D 2.2 x 10-1 E 11.4 x 1012 F .41 x 103

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Answer D

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300,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000, 000,000,000 kg (How do you even say that number?)

The mass of the solar system Slide 35 / 127 More Practice Slide 36 / 127 Express 9,040,000,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit. Answer

Slide 36 (Answer) / 127

Express 9,040,000,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit.

[This object is a pull tab]

Answer 9.04 x 10

9

Slide 37 / 127

Express 13,030,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit. Answer

Slide 37 (Answer) / 127

Express 13,030,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit.

[This object is a pull tab]

Answer 13.03 x 10

7

Slide 38 / 127

Express 1,000,000,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit. Answer

Slide 38 (Answer) / 127

Express 1,000,000,000 in scientific notation

• 1. Write the number without the comma.
• 2. Place the decimal so that the first number

will be less than 10 but greater than or equal to 1.

• 3. Count how many places you had to move

the decimal point. This becomes the exponent

• f 10.
• 4. Drop the zeros to the right of the right-most

non-zero digit.

[This object is a pull tab]

Answer 1 x 10

9

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11 Which of the following is 12,300,000 in scientific notation? A .123 x 108 B 1.23 x 105 C 123 x 105 D 1.23 x 107

Answer

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11 Which of the following is 12,300,000 in scientific notation? A .123 x 108 B 1.23 x 105 C 123 x 105 D 1.23 x 107

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Answer D

Slide 40 / 127 Writing Small Numbers in Scientific Notation Slide 41 / 127 Express 0.0043 in scientific notation

0043 0043 x 10

.

? 0043 x 10

.

1 2 3

? 4.3 x 10-3

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit.

Slide 42 / 127

Express 0.00000832 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit. Answer

Slide 42 (Answer) / 127

Express 0.00000832 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit.

[This object is a pull tab]

Answer 8.32 x 10

• 6

Slide 43 / 127 Express 0.0073 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit. Answer

Slide 43 (Answer) / 127 Express 0.0073 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit.

[This object is a pull tab]

Answer 7.3 x 10

• 3

Slide 44 / 127

12 Which is the correct decimal placement to convert 0.000832 to scientific notation? A 832 B 83.2 C .832 D 8.32

Answer

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12 Which is the correct decimal placement to convert 0.000832 to scientific notation? A 832 B 83.2 C .832 D 8.32

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Answer D

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13 Which is the correct decimal placement to convert 0.000000376 to scientific notation? A 3.76 B 0.376 C 376. D 37.6

Answer

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13 Which is the correct decimal placement to convert 0.000000376 to scientific notation? A 3.76 B 0.376 C 376. D 37.6

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Answer A

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14 How many times do you need to move the decimal point to change 0.00658 to 6.58? A 2 B 3 C 4 D 5

Answer

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14 How many times do you need to move the decimal point to change 0.00658 to 6.58? A 2 B 3 C 4 D 5

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Answer B

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15 How many times do you need to move the decimal point to change 0.000003242 to 3.242? A 5 B 6 C 7 D 8

Answer

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15 How many times do you need to move the decimal point to change 0.000003242 to 3.242? A 5 B 6 C 7 D 8

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Answer B

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16 Write 0.00278 in scientific notation. A 27.8 x 10-4 B 2.78 x 103 C 2.78 x 10-3 D 278 x 10-3

Answer

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16 Write 0.00278 in scientific notation. A 27.8 x 10-4 B 2.78 x 103 C 2.78 x 10-3 D 278 x 10-3

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Answer C

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17 Which of these is the only number larger than 1 in scientific notation? A .34 x 10-8 B 7.2 x 10-3 C 8.9 x 104 D 2.2 x 10-1 E 11.4 x 10-12 F .41 x 10-3

Answer

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17 Which of these is the only number larger than 1 in scientific notation? A .34 x 10-8 B 7.2 x 10-3 C 8.9 x 104 D 2.2 x 10-1 E 11.4 x 10-12 F .41 x 10-3

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Answer C

Slide 50 / 127 More Practice Slide 51 / 127 Express 0.001003 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit. Answer

Slide 51 (Answer) / 127 Express 0.001003 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit.

[This object is a pull tab]

Answer 1.003 x 10

• 3

Slide 52 / 127 Express 0.000902 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit. Answer

Slide 52 (Answer) / 127 Express 0.000902 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit.

[This object is a pull tab]

Answer 9.02 x 10

• 4

Slide 53 / 127 Express 0.0000012 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit. Answer

Slide 53 (Answer) / 127 Express 0.0000012 in scientific notation

• 1. Write the number without the decimal point.
• 2. Place the decimal so that the first number is 1 or

more, but less than 10.

• 3. Count how many places you had to move the

decimal point. The negative of this numbers becomes the exponent of 10.

• 4. Drop the zeros to the left of the left-most non-

zero digit.

[This object is a pull tab]

Answer 1.2 x 10

• 6

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18 Write 0.000847 in scientific notation. A 8.47 x 104 B 847 x 10-4 C 8.47 x 10-4 D 84.7 x 10-5

Answer

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18 Write 0.000847 in scientific notation. A 8.47 x 104 B 847 x 10-4 C 8.47 x 10-4 D 84.7 x 10-5

[This object is a pull tab]

Answer C

Slide 55 / 127 Converting to Standard Form

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Slide 56 / 127 Express 3.5 x 10 4 in standard form

35,000

• 1. Write the coefficient.
• 2. Add a number of zeros equal to the

exponent: to the right for positive exponents and to the left for negative.

• 3. Move the decimal the number of places

indicated by the exponent: to the right for positive exponents and to the left for negative.

• 4. Drop unnecessary zeros and add

comma, as necessary.

3.50000 3.5 35000.0

Slide 57 / 127 Express 1.02 x 10 6 in standard form

• 1. Write the coefficient.
• 2. Add a number of zeros equal to the

exponent: to the right for positive exponents and to the left for negative.

• 3. Move the decimal the number of places

indicated by the exponent: to the right for positive exponents and to the left for negative.

• 4. Drop unnecessary zeros and add

comma, as necessary. Answer

Slide 57 (Answer) / 127 Express 1.02 x 10 6 in standard form

• 1. Write the coefficient.
• 2. Add a number of zeros equal to the

exponent: to the right for positive exponents and to the left for negative.

• 3. Move the decimal the number of places

indicated by the exponent: to the right for positive exponents and to the left for negative.

• 4. Drop unnecessary zeros and add

comma, as necessary.

[This object is a pull tab]

Answer 1,020,000

Slide 58 / 127 Express 3.42 x 10 -3 in standard form

• 1. Write the coefficient.
• 2. Add a number of zeros equal to the

exponent: to the right for positive exponents and to the left for negative.

• 3. Move the decimal the number of places

indicated by the exponent: to the right for positive exponents and to the left for negative.

• 4. Drop unnecessary zeros and add

comma, as necessary. Answer

Slide 58 (Answer) / 127 Express 3.42 x 10 -3 in standard form

• 1. Write the coefficient.
• 2. Add a number of zeros equal to the

exponent: to the right for positive exponents and to the left for negative.

• 3. Move the decimal the number of places

indicated by the exponent: to the right for positive exponents and to the left for negative.

• 4. Drop unnecessary zeros and add

comma, as necessary.

[This object is a pull tab]

Answer 0.00342

Slide 59 / 127 Express 2.95 x 10 -4 in standard form

• 1. Write the coefficient.
• 2. Add a number of zeros equal to the

exponent: to the right for positive exponents and to the left for negative.

• 3. Move the decimal the number of places

indicated by the exponent: to the right for positive exponents and to the left for negative.

• 4. Drop unnecessary zeros and add

comma, as necessary. Answer

Slide 59 (Answer) / 127 Express 2.95 x 10 -4 in standard form

• 1. Write the coefficient.
• 2. Add a number of zeros equal to the

exponent: to the right for positive exponents and to the left for negative.

• 3. Move the decimal the number of places

indicated by the exponent: to the right for positive exponents and to the left for negative.

• 4. Drop unnecessary zeros and add

comma, as necessary.

[This object is a pull tab]

Answer 0.000295

Slide 60 / 127

19 How many times do you need to move the decimal and which direction to change 7.41 x 10 -6 into standard form? A 6 to the right B 6 to the left C 7 to the right D 7 to the left

Answer

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19 How many times do you need to move the decimal and which direction to change 7.41 x 10 -6 into standard form? A 6 to the right B 6 to the left C 7 to the right D 7 to the left

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Answer B

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20 How many times do you need to move the decimal and which direction to change 4.5 x 10 10 into standard form? A 10 to the right B 10 to the left C 11 to the right D 11 to the left

Answer

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20 How many times do you need to move the decimal and which direction to change 4.5 x 10 10 into standard form? A 10 to the right B 10 to the left C 11 to the right D 11 to the left

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Answer A

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21 Write 6.46 x 10 4 in standard form. A 646,000 B 0.00000646 C 64,600 D 0.0000646

Answer

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21 Write 6.46 x 10 4 in standard form. A 646,000 B 0.00000646 C 64,600 D 0.0000646

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Answer C

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22 Write 3.4 x 10 3 in standard form. A 3,400 B 340 C 34,000 D 0.0034

Answer

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22 Write 3.4 x 10 3 in standard form. A 3,400 B 340 C 34,000 D 0.0034

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Answer A

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23 Write 6.46 x 10 -5 in standard form. A 646,000 B 0.00000646 C 0.00646 D 0.0000646

Answer

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23 Write 6.46 x 10 -5 in standard form. A 646,000 B 0.00000646 C 0.00646 D 0.0000646

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Answer D

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24 Write 1.25 x 10 -4 in standard form. A 125 B 0.000125 C 0.00000125 D 4.125

Answer

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24 Write 1.25 x 10 -4 in standard form. A 125 B 0.000125 C 0.00000125 D 4.125

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Answer B

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25 Write 4.56 x 10 -2 in standard form. A 456 B 4560 C 0.00456 D 0.0456

Answer

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25 Write 4.56 x 10 -2 in standard form. A 456 B 4560 C 0.00456 D 0.0456

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Answer D

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26 Write 1.01 x 10 9 in standard form. A 101,000,000,000 B 1,010,000,000 C 0.00000000101 D 0.000000101

Answer

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26 Write 1.01 x 10 9 in standard form. A 101,000,000,000 B 1,010,000,000 C 0.00000000101 D 0.000000101

[This object is a pull tab]

Answer B

Slide 68 / 127 Magnitude

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Slide 69 / 127

Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10. Why? This is due to magnitude. Magnitude is how we can observe very large or very small numbers and easily compare them. The magnitude of a number is the exponent when the number is written in scientific notation. Below are a few examples. 8304 = 8.304 x 103 - the order of magnitude is 3 20,000 = 2 x 104 – the order of magnitude is 4 0.000034 = 3.4 x 10-5 – the order of magnitude is -5

Magnitude

Slide 70 / 127

Write each of the following in Scientific Notation first and then indicate the order of magnitude.

6214 472.17 813000000 .000253 .00647 .00000049

Scientific Notation Order of Magnitude

Slide 71 / 127 Application

Let J represent the world population in 1950. J = 2,556,000,053. Find the smallest power of 10 that will exceed J. The number above (J) has 10 digits and is smaller than a whole number with 11 digits. (10,000,000,000 or 1010 therefore J<1010) The answer is 10.

Slide 72 / 127 Application

Let K represent the national debt in 1950. K = 257,357,352,351. Find the smallest power of 10 that will exceed K. Answer

Slide 72 (Answer) / 127 Application

Let K represent the national debt in 1950. K = 257,357,352,351. Find the smallest power of 10 that will exceed K.

[This object is a pull tab]

Answer The number above (K) has 12 digits and is smaller than a whole number with 13 digits. (1,000,000,000,000 or 1012 therefore J<1012) The answer is 12.

Slide 73 / 127

27 If m = 149,162,536,496,481,100 find the smallest power of 10 that will exceed m.

Derived from

( (

Answer

Slide 73 (Answer) / 127

27 If m = 149,162,536,496,481,100 find the smallest power of 10 that will exceed m.

Derived from

( (

[This object is a pull tab]

Answer

18

The number has 18 digits. So the smallest power of 10 that will exceed m is 1018 or 1,000,000,000,000,000,000

Slide 74 / 127

28 What is the smallest power of 10 that will exceed 5,321?

Derived from

( (

Answer

Slide 74 (Answer) / 127

28 What is the smallest power of 10 that will exceed 5,321?

Derived from

( (

[This object is a pull tab]

Answer

4

The number has 4 digits. So the smallest power of 10 that will exceed m is 104 or 10,000

Slide 75 / 127

29 If m = 628 find the smallest power of 10 that will exceed m?

Derived from

( (

Answer

Slide 75 (Answer) / 127

29 If m = 628 find the smallest power of 10 that will exceed m?

Derived from

( (

[This object is a pull tab]

Answer

3

The number has 3 digits. So the smallest power of 10 that will exceed m is 103 or 1,000

Slide 76 / 127

30 What would the negative exponent be used to express the number ?

Derived from

( (

Answer

Slide 76 (Answer) / 127

30 What would the negative exponent be used to express the number ?

Derived from

( (

[This object is a pull tab]

Answer

• 4

Slide 77 / 127

31 The chance of a shark bite is and the chance

• f dying from a snake bite is which are more

likely to be bit by? A both a the same B the snake C the shark D neither

Derived from

( (

Answer

Slide 77 (Answer) / 127

31 The chance of a shark bite is and the chance

• f dying from a snake bite is which are more

likely to be bit by? A both a the same B the snake C the shark D neither

Derived from

( (

[This object is a pull tab]

Answer C

Slide 78 / 127 Comparing Numbers Written in Scientific Notation

Return to Table of Contents

Slide 79 / 127

Click for web site

Slide 80 / 127

First, compare the exponents. If the exponents are different, the coefficients don't matter; they have a smaller effect. Whichever number has the larger exponent is the larger number.

Comparing numbers in scientific notation Slide 81 / 127 Comparing numbers in scientific notation < >

9.99 x 10 3 2.17 x 10 4 1.02 x 10 2 8.54 x 10 -3 6.83 x 10 -9 3.93 x 10 -2

=

When the exponents are different, just compare the exponents.

=

just drag the sign that is correct

Answer

Answer

Slide 81 (Answer) / 127 Comparing numbers in scientific notation < >

9.99 x 10 3 2.17 x 10 4 1.02 x 10 2 8.54 x 10 -3 6.83 x 10 -9 3.93 x 10 -2

=

When the exponents are different, just compare the exponents.

=

just drag the sign that is correct

Answer [This object is a pull tab]

Answer

<, >, <

Slide 82 / 127

If the exponents are the same, compare the coefficients. The larger the coefficient, the larger the number (if the exponents are the same).

Comparing numbers in scientific notation Slide 83 / 127 Comparing numbers in scientific notation

5.67 x 10

3

4.67 x 10

3

When the exponents are the same, just compare the coefficients. 4.32 x 106 4.67 x 10

6

2.32 x 1010 3.23 x 1010

< > =

Answer

Slide 83 (Answer) / 127 Comparing numbers in scientific notation

5.67 x 10

3

4.67 x 10

3

When the exponents are the same, just compare the coefficients. 4.32 x 106 4.67 x 10

6

2.32 x 1010 3.23 x 1010

< > =

[This object is a pull tab]

Answer >, <, <

Slide 84 / 127

32 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, I, II, IV

• I. 1.0 x 105
• II. 7.5 x 10 6
• III. 8.3 x 10 4
• IV. 5.4 x 107

Answer

Slide 84 (Answer) / 127

32 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, I, II, IV

• I. 1.0 x 105
• II. 7.5 x 10 6
• III. 8.3 x 10 4
• IV. 5.4 x 107

[This object is a pull tab]

Answer D

Slide 85 / 127

33 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D I, II, IV, III

• I. 1.0 x 102
• II. 7.5 x 106
• III. 8.3 x 109
• IV. 5.4 x 107

Answer

Slide 85 (Answer) / 127

33 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D I, II, IV, III

• I. 1.0 x 102
• II. 7.5 x 106
• III. 8.3 x 109
• IV. 5.4 x 107

[This object is a pull tab]

Answer D

Slide 86 / 127

34 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C III, IV, II, I D III, IV, I, II

• I. 1 x 102
• II. 7.5 x 10

3

• III. 8.3 x 10
• 2
• IV. 5.4 x 10
• 3

Answer

Slide 86 (Answer) / 127

34 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C III, IV, II, I D III, IV, I, II

• I. 1 x 102
• II. 7.5 x 10

3

• III. 8.3 x 10
• 2
• IV. 5.4 x 10
• 3

[This object is a pull tab]

Answer B

Slide 87 / 127

35 Which is ordered from least to greatest? A II, III, I, IV B IV, III, I, II C III, IV, II, I D III, IV, I, II

• I. 1 x 10-2
• II. 7.5 x 10-24
• III. 8.3 x 10-15
• IV. 5.4 x 10

2

Answer

Slide 87 (Answer) / 127

35 Which is ordered from least to greatest? A II, III, I, IV B IV, III, I, II C III, IV, II, I D III, IV, I, II

• I. 1 x 10-2
• II. 7.5 x 10-24
• III. 8.3 x 10-15
• IV. 5.4 x 10

2

[This object is a pull tab]

Answer A

Slide 88 / 127

36 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 1.0 x 102
• II. 7.5 x 102
• III. 8.3 x 102
• IV. 5.4 x 10

2

Answer

Slide 88 (Answer) / 127

36 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 1.0 x 102
• II. 7.5 x 102
• III. 8.3 x 102
• IV. 5.4 x 10

2

[This object is a pull tab]

Answer C

Slide 89 / 127

37 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 1.0 x 106
• II. 7.5 x 10

6

• III. 8.3 x 10

6

• IV. 5.4 x 10

7

Answer

Slide 89 (Answer) / 127

37 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 1.0 x 106
• II. 7.5 x 10

6

• III. 8.3 x 10

6

• IV. 5.4 x 10

7

[This object is a pull tab]

Answer A

Slide 90 / 127

38 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 1.0 x 103
• II. 5.0 x 10

3

• III. 8.3 x 10

6

• IV. 9.5 x 10

6

Answer

Slide 90 (Answer) / 127

38 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 1.0 x 103
• II. 5.0 x 10

3

• III. 8.3 x 10

6

• IV. 9.5 x 10

6

[This object is a pull tab]

Answer A

Slide 91 / 127

39 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 2.5 x 10-3
• II. 5.0 x 10
• 3
• III. 9.2 x 10
• 6
• IV. 4.2 x 10
• 6

Answer

Slide 91 (Answer) / 127

39 Which is ordered from least to greatest? A I, II, III, IV B IV, III, I, II C I, IV, II, III D III, IV, I, II

• I. 2.5 x 10-3
• II. 5.0 x 10
• 3
• III. 9.2 x 10
• 6
• IV. 4.2 x 10
• 6

[This object is a pull tab]

Answer D

Slide 92 / 127 Multiplying Numbers in Scientific Notation

Multiplying with scientific notation requires at least three (and sometimes four) steps.

• 1. Multiply the coefficients
• 2. Multiply the powers of ten
• 3. Combine those results
• 4. Put in proper form

Return to Table of Contents

Slide 93 / 127

6.0 x 2.5 = 15 104 x 102 = 106 15 x 106 1.5 x 107

• 1. Multiply the coefficients
• 2. Multiply the powers of ten
• 3. Combine those results
• 4. Put in proper form

Evaluate: (6.0 x 104)(2.5 x 102)

Multiplying Numbers in Scientific Notation Slide 94 / 127

• 1. Multiply the coefficients
• 2. Multiply the powers of ten
• 3. Combine those results
• 4. Put in proper form

Evaluate: (4.80 x 106 )(9.0 x 10-8 )

Multiplying Numbers in Scientific Notation

Answer

Slide 94 (Answer) / 127

• 1. Multiply the coefficients
• 2. Multiply the powers of ten
• 3. Combine those results
• 4. Put in proper form

Evaluate: (4.80 x 106 )(9.0 x 10-8 )

Multiplying Numbers in Scientific Notation

[This object is a pull tab]

Answer 4.32 x 10-1

Slide 95 / 127

40 Evaluate (2.0 x 10-4)(4.0 x 107). Express

the result in scientific notation.

A 8.0 x 1011 B 8.0 x 103 C 5.0 x 103 D 5.0 x 1011 E 7.68 x 10-28 F 7.68 x 10-28

Answer

Slide 95 (Answer) / 127

40 Evaluate (2.0 x 10-4)(4.0 x 107). Express

the result in scientific notation.

A 8.0 x 1011 B 8.0 x 103 C 5.0 x 103 D 5.0 x 1011 E 7.68 x 10-28 F 7.68 x 10-28

[This object is a pull tab]

Answer B

Slide 96 / 127

41 Evaluate (5.0 x 106)(7.0 x 107) A 3.5 x 1013 B 3.5 x 1014 C 3.5 x 101 D 3.5 x 10-1 E 7.1 x 1013 F 7.1 x 101

Answer

Slide 96 (Answer) / 127

41 Evaluate (5.0 x 106)(7.0 x 107) A 3.5 x 1013 B 3.5 x 1014 C 3.5 x 101 D 3.5 x 10-1 E 7.1 x 1013 F 7.1 x 101

[This object is a pull tab]

Answer B

Slide 97 / 127

42 Evaluate (6.0 x 102)(2.0 x 103) A 1.2 x 106 B 1.2 x 101 C 1.2 x 105 D 3.0 x 10-1 E 3.0 x 105 F 3.0 x 101

Answer

Slide 97 (Answer) / 127

42 Evaluate (6.0 x 102)(2.0 x 103) A 1.2 x 106 B 1.2 x 101 C 1.2 x 105 D 3.0 x 10-1 E 3.0 x 105 F 3.0 x 101

[This object is a pull tab]

Answer A

Slide 98 / 127

43 Evaluate (1.2 x 10-6)(2.5 x 103). Express the result in scientific notation. A 3 x 103 B 3 x 10-3 C 30 x 10-3 D 0.3 x 10-18 E 30 x 1018

Answer

Slide 98 (Answer) / 127

43 Evaluate (1.2 x 10-6)(2.5 x 103). Express the result in scientific notation. A 3 x 103 B 3 x 10-3 C 30 x 10-3 D 0.3 x 10-18 E 30 x 1018

[This object is a pull tab]

Answer B

Slide 99 / 127

44 Evaluate (1.1 x 104)(3.4 x 106). Express the result in scientific notation. A 3.74 x 10

24

B 3.74 x 10

10

C 4.5 x 1024 D 4.5 x 10

10

E 37.4 x 10

24

Answer

Slide 99 (Answer) / 127

44 Evaluate (1.1 x 104)(3.4 x 106). Express the result in scientific notation. A 3.74 x 10

24

B 3.74 x 10

10

C 4.5 x 1024 D 4.5 x 10

10

E 37.4 x 10

24

[This object is a pull tab]

Answer B

Slide 100 / 127

45 Evaluate (3.3 x 104)(9.6 x 103). Express the result in scientific notation. A 31.68 x 10 7 B 3.168 x 10 8 C 3.2 x 107 D 32 x 108 E 30 x 107

Answer

Slide 100 (Answer) / 127

45 Evaluate (3.3 x 104)(9.6 x 103). Express the result in scientific notation. A 31.68 x 10 7 B 3.168 x 10 8 C 3.2 x 107 D 32 x 108 E 30 x 107

[This object is a pull tab]

Answer B

Slide 101 / 127

46 Evaluate (2.2 x 10-5)(4.6 x 10-4). Express the result in scientific notation. A 10.12 x 10 -20 B 10.12 x 10 -9 C 1.012 x 10 -10 D 1.012 x 10 -9 E 1.012 x 10 -8

Answer

Slide 101 (Answer) / 127

46 Evaluate (2.2 x 10-5)(4.6 x 10-4). Express the result in scientific notation. A 10.12 x 10 -20 B 10.12 x 10 -9 C 1.012 x 10 -10 D 1.012 x 10 -9 E 1.012 x 10 -8

[This object is a pull tab]

Answer E

Slide 102 / 127 Dividing Numbers in Scientific Notation

Dividing with scientific notation follows the same basic rules as multiplying.

• 1. Divide the coefficients
• 2. Divide the powers of

ten

• 3. Combine those results
• 4. Put in proper form

Slide 103 / 127 Division with Scientific Notation

5.4 ÷ 9.0 = 0.6 106 ÷ 102 = 104

0.6 x 10 4

6.0 x 103

• 1. Divide the coefficients
• 2. Divide the powers of ten
• 3. Combine those results
• 4. Put in proper form

Evaluate: 9.0 x 102 5.4 x 106

Slide 104 / 127 Division with Scientific Notation

• 1. Divide the coefficients
• 2. Divide the powers of ten
• 3. Combine those results
• 4. Put in proper form

Evaluate: 1.1 x 10-3 4.4 x 106 Answer

Slide 104 (Answer) / 127 Division with Scientific Notation

• 1. Divide the coefficients
• 2. Divide the powers of ten
• 3. Combine those results
• 4. Put in proper form

Evaluate: 1.1 x 10-3 4.4 x 106

[This object is a pull tab]

Answer 4 x 109

Slide 105 / 127

47 Evaluate 4.16 x 10 -9 5.2 x 10 -5 Express the result in scientific notation. A 0.8 x 10-4 B 0.8 x 10-14 C 0.8 x 10-5 D 8 x 10-4 E 8 x 10-5

Answer

Slide 105 (Answer) / 127

47 Evaluate 4.16 x 10 -9 5.2 x 10 -5 Express the result in scientific notation. A 0.8 x 10-4 B 0.8 x 10-14 C 0.8 x 10-5 D 8 x 10-4 E 8 x 10-5

[This object is a pull tab]

Answer E

Slide 106 / 127

48 Evaluate 7.6 x 10 -2 4 x 10 -4 Express the result in scientific notation. A 1.9 x 10-2 B 1.9 x 10-6 C 1.9 x 102 D 1.9 x 10-8 E 1.9 x 108

Answer

Slide 106 (Answer) / 127

48 Evaluate 7.6 x 10 -2 4 x 10 -4 Express the result in scientific notation. A 1.9 x 10-2 B 1.9 x 10-6 C 1.9 x 102 D 1.9 x 10-8 E 1.9 x 108

[This object is a pull tab]

Answer C

Slide 107 / 127

49 Evaluate 8.2 x 10 3 2 x 10 7 Express the result in scientific notation. A 4.1 x 10-10 B 4.1 x 104 C 4.1 x 10-4 D 4.1 x 1021 E 4.1 x 1010

Answer

Slide 107 (Answer) / 127

49 Evaluate 8.2 x 10 3 2 x 10 7 Express the result in scientific notation. A 4.1 x 10-10 B 4.1 x 104 C 4.1 x 10-4 D 4.1 x 1021 E 4.1 x 1010

[This object is a pull tab]

Answer C

Slide 108 / 127

50 Evaluate 3.2 x 10 -2 6.4 x 10 -4 Express the result in scientific notation. A .5 x 10-6 B .5 x 10-2 C .5 x 102 D 5 x 101 E 5 x 103

Answer

Slide 108 (Answer) / 127

50 Evaluate 3.2 x 10 -2 6.4 x 10 -4 Express the result in scientific notation. A .5 x 10-6 B .5 x 10-2 C .5 x 102 D 5 x 101 E 5 x 103

[This object is a pull tab]

Answer D

Slide 109 / 127

51 The point on a pin has a diameter of approximately 1 x 10-4 meters. If an atom has a diameter of 2 x 10-10 meters, about how many atoms could fit across the diameter of the point of a pin?

A

50,000

B

500,000

C

2,000,000

D

5,000,000

Question from ADP Algebra I End-of-Course Practice Test

Answer

Slide 109 (Answer) / 127

51 The point on a pin has a diameter of approximately 1 x 10-4 meters. If an atom has a diameter of 2 x 10-10 meters, about how many atoms could fit across the diameter of the point of a pin?

A

50,000

B

500,000

C

2,000,000

D

5,000,000

Question from ADP Algebra I End-of-Course Practice Test [This object is a pull tab]

Answer B

Slide 110 / 127 Addition and Subtraction with Scientific Notation

Numbers in scientific notation can only be added or subtracted if they have the same exponents. If needed, an intermediary step is to rewrite one of the numbers so it has the same exponent as the other. Return to Table of Contents

Slide 111 / 127 Addition and Subtraction

This is the simplest example of addition 4.0 x 103 + 5.3 x 103 = Since the exponents are the same (3), just add the coefficients. 4.0 x 103 + 5.3 x 103 = 9.3 x 103 4.0 thousand + 5.3 thousand 9.3 thousand. This just says

Slide 112 / 127 Addition and Subtraction

This problem is slightly more difficult because you need to add

• ne extra step at the end.

8.0 x 103 + 5.3 x 103 = Since the exponents are the same (3), just add the coefficients. 8.0 x 103 + 5.3 x 103 = 13.3 x 103 But that is not proper form, since 13.3 > 10; it should be written as 1.33 x 104

Slide 113 / 127 Addition and Subtraction

8.0 x 104 + 5.3 x 103 = This requires an extra step at the beginning because the exponents are different. We have to either convert the first number to 80 x 103 or the second one to 0.53 x 104. The latter approach saves us a step at the end. 8.0 x 104 + 0.53 x 104 = 8.53 x 104 Once both numbers had the same exponents, we just add the

• coefficient. Note that when we made the exponent 1 bigger,

that's makes the number 10x bigger; we had to make the coefficient 1/10 as large to keep the number the same.

Slide 114 / 127

52 The sum of 5.6 x 10 3 and 2.4 x 10 3 is A 8.0 x 103 B 8.0 x 106 C 8.0 x 10-3 D 8.53 x 103

Answer

Slide 114 (Answer) / 127

52 The sum of 5.6 x 10 3 and 2.4 x 10 3 is A 8.0 x 103 B 8.0 x 106 C 8.0 x 10-3 D 8.53 x 103

[This object is a pull tab]

Answer A

Slide 115 / 127

53 8.0 x 103 minus 2.0 x 103 is A 6.0 x 10-3 B 6.0 x 100 C 6.0 x 103 D 7.8 x 103

Answer

Slide 115 (Answer) / 127

53 8.0 x 103 minus 2.0 x 103 is A 6.0 x 10-3 B 6.0 x 100 C 6.0 x 103 D 7.8 x 103

[This object is a pull tab]

Answer C

Slide 116 / 127

54 7.0 x 103 plus 2.0 x 102 is A 9.0 x 103 B 9.0 x 105 C 7.2 x 103 D 7.2 x 102

Answer

Slide 116 (Answer) / 127

54 7.0 x 103 plus 2.0 x 102 is A 9.0 x 103 B 9.0 x 105 C 7.2 x 103 D 7.2 x 102

[This object is a pull tab]

Answer C

Slide 117 / 127

55 3.5 x 105 plus 7.8 x 105 is A 11.3 x 105 B 1.13 x 104 C 1.13 x 106 D 11.3 x 1010

Answer

Slide 117 (Answer) / 127

55 3.5 x 105 plus 7.8 x 105 is A 11.3 x 105 B 1.13 x 104 C 1.13 x 106 D 11.3 x 1010

[This object is a pull tab]

Answer C

Slide 118 / 127

Glossary

Return to Table of Contents

Slide 119 / 127

Back to Instruction

Base

The number that is going to be raised to a power. It is multiplied the number of times the power equals.

73 188 29 2154 335 112

ten to the power of 3 103 = 10 x 10 x 10 = 1,000

In scientific notation, the base will always = 10

Slide 120 / 127

Back to Instruction

Coefficient

A number used to multiply a variable. A factor of a term.

3y 6.5 x 103 19z

.000000459 4.59 x 10-7

3.78 x 106

scientific notation:

a coefficient

and 10 raised to some power

Slide 121 / 127

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Power

a.k.a. Exponent

• r

Index

ten to the power of 3 103 = 10 x 10 x 10 = 1,000 3.78 x 106

scientific notation:

a coefficient and 10 raised to

some power

A number that shows you how many times to use the number in a multiplication. A quick way to write repeated multiplication.

Slide 122 / 127

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Scientific Notation

A convenient system scientists developed that rewrites big or small numbers using powers of 10 that does not change the value.

3.78 x 106 a coefficient and 10 raised to some power.

small numbers 0.00015 kg = 1.5 x 10-4 big numbers 180,000 kg = 1.8 x

105

Blue Whale

Slide 123 / 127

Back to Instruction

Standard Form

4,500,000 0.00000032 120,000 0.006789

Standard Form: vs. Scientific Form:

6.5 x 103

6,500

*Note* this is not the "correct" form but the most recognizable form.

The most familiar form of a number. A number whose scientific form has been expanded. Slide 124 / 127

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Slide 125 / 127

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Slide 126 / 127

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Slide 127 / 127

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