Slide 1 / 137 Slide 2 / 137 8th Grade Scientific Notation 2015-11-20 www.njctl.org Slide 3 / 137 Slide 3 (Answer) / 137 Table of Contents Table of Contents Click on the topic to go to that section Click on the topic to go to that section Purpose of Scientific Notation Purpose of Scientific Notation · · Writing Numbers in Scientific Notation Writing Numbers in Scientific Notation · · Vocabulary Words are bolded Converting Between Scientific Notation and Standard Form Converting Between Scientific Notation and Standard Form Teacher Notes · · in the presentation. The text Magnitude Magnitude · · box the word is in is then Comparing Numbers in Scientific Notation Comparing Numbers in Scientific Notation · · linked to the page at the end of the presentation with the Multiply and Divide with Scientific Notation Multiply and Divide with Scientific Notation · · word defined on it. Addition and Subtraction with Scientific Notation Addition and Subtraction with Scientific Notation · · Glossary Glossary · · [This object is a pull tab] Slide 4 / 137 Slide 5 / 137 Purpose of Scientific Notation 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 Purpose of Can you guess what weighs this much? Scientific Notation Return to Table of Contents
Slide 6 / 137 Slide 7 / 137 Can you match these Can you match these BIG objects to their weights? BIG objects to their weights? The Earth The Great Pyramid at Giza The Earth The Great Pyramid at Giza 300,000,000,000 kg Click object to reveal 600,000,000 kg answer 60,000,000,000,000, 2,000,000,000,000,000,0 000,000,000,000 kg 00,000,000,000,000 kg Blue Whale - largest animal on earth Blue Whale - largest animal on earth 600,000,000 kg 180,000 kg 60,000,000,000,000, The Sun The Sun 000,000,000,000 kg Total Human Population Total Human Population 2,000,000,000,000,000,0 180,000 kg 00,000,000,000,000 kg 300,000,000,000 kg Slide 8 / 137 Slide 9 / 137 grain of sand grain of sand Can you match these small Click to reveal the answers. objects to their weights? 0.00000000035 kg molecule molecule 0.00015 kg 0.000000000000000000000000030 kg 0.000000000000000000000000030 kg 0.00000000035 kg steam steam 0.00015 kg Slide 10 / 137 Slide 11 / 137 Scientific Notation Scientific Notation The examples were written in standard form , the form we Scientific Notation uses Powers of 10 to write big or small normally use. But the standard form is difficult to work with numbers more conveniently. when a number is HUGE or tiny , if it has a lot of zeros. Using scientific notation requires us to use the rules of Scientists have come up with a more convenient method to exponents we learned earlier. While we developed those write very LARGE and very small numbers. rules for all bases , scientific notation only uses base 10. Writing numbers in scientific notation doesn't change the value of the number.
Slide 12 / 137 Slide 13 / 137 Powers of Ten Powers of Integers 10 1 = 10 Powers are a quick way to write repeated multiplication, just as 10 2 = 10 x 10 = 100 multiplication was a quick way to write repeated addition. 10 3 = 10 x 10 x 10 = 1,000 These are all equivalent: 10 4 = 10 x 10 x 10 x 10 = 10,000 10 3 10 5 = 10 x 10 x 10 x 10 x 10 = 100,000 (10)(10)(10) 1000 Click here to see a video on powers of ten which puts our universe into perspective! In this case, the base is 10 and the exponent is 3. Click here to move from the Milky Way through space towards Earth to an oak tree, and then within a cell! Slide 14 / 137 Slide 15 / 137 Review of Exponent Rules 10 2 x 10 4 = 1 A 10 6 Remember that when multiplying numbers with exponents, if the bases are the same, you write B 10 8 the base and add the exponents. C 10 10 2 5 x 2 6 = 2 (5+6) = 2 11 D 10 12 3 3 x 3 7 = 3 (3+7) = 3 10 10 8 x 10 -3 = 10 (8+-3) = 10 5 4 7 x 4 -7 = 4 (7+-7) = 4 0 = 1 Slide 15 (Answer) / 137 Slide 16 / 137 1 10 2 x 10 4 = 2 10 14 x 10 -6 = 10 6 A A 10 6 Answer B 10 8 B 10 8 A C 10 10 C 10 10 D 10 12 D 10 12 [This object is a pull tab]
Slide 16 (Answer) / 137 Slide 17 / 137 2 10 14 x 10 -6 = 3 10 -4 x 10 -6 = 10 6 A A 10 -6 B 10 8 Answer B 10 -8 B C 10 10 C 10 -10 D 10 12 D 10 -12 [This object is a pull tab] Slide 17 (Answer) / 137 Slide 18 / 137 10 -4 x 10 -6 = 10 4 x 10 6 = 3 4 10 -6 A A 10 6 B 10 -8 Answer B 10 8 C C 10 -10 C 10 10 D 10 -12 D 10 12 [This object is a pull tab] Slide 18 (Answer) / 137 Slide 19 / 137 4 10 4 x 10 6 = A 10 6 Answer B 10 8 C C 10 10 Writing Numbers in D 10 12 Scientific Notation [This object is a pull tab] Return to Table of Contents
Slide 20 / 137 Slide 21 / 137 Scientific Notation Scientific Notation Here are some different ways of writing 6,500. 6.5 x 10 3 isn't a lot more convenient than 6,500. 6,500 = 6.5 thousand But let's do the same thing with 7,400,000,000 6.5 thousand = 6.5 x 1,000 which is equal to 7.4 billion 6.5 x 1,000 = 6.5 x 10 3 which is 7.4 x 1,000,000,000 which is 7.4 x 10 9 which means that 6,500 = 6.5 x 10 3 Besides being shorter than 7,400,000,000 it is a lot 6,500 is standard form of the number easier to keep track of the zeros in scientific notation. and 6.5 x 10 3 is scientific notation And we'll see that the math gets a lot easier as well. These are two ways of writing the same number. Slide 22 / 137 Slide 23 / 137 Express 870,000 in Scientific Notation Scientific Notation Scientific notation expresses numbers as the product of: Write the number without the comma. 870000 1. a coefficient and 10 raised to some power. 2. Place the decimal so that the first 8 . 70000 x 10 number will be less than 10 but 3.78 x 10 6 greater than or equal to 1. The coefficient is always greater than or equal to one, and less than 3. Count how many places you had 10. In this case, the number 3,780,000 is expressed in scientific 8 . 70000 x 10 to move the decimal point. This notation. 5 4 3 2 1 becomes the exponent of 10. 4. Drop the zeros to the right of the 8.7 x 10 5 right-most non-zero digit. Slide 24 / 137 Slide 24 (Answer) / 137 Express 53,600 in Scientific Notation Express 53,600 in Scientific Notation 1. Write the number without the comma. 1. Write the number without the comma. 2. 2. Place the decimal so that the first Place the decimal so that the first number will be less than 10 but number will be less than 10 but Answer greater than or equal to 1. greater than or equal to 1. 5.36 x 10 4 3. 3. Count how many places you had Count how many places you had to move the decimal point. This to move the decimal point. This becomes the exponent of 10. becomes the exponent of 10. 4. Drop the zeros to the right of the 4. Drop the zeros to the right of the [This object is a pull tab] right-most non-zero digit. right-most non-zero digit.
Slide 25 / 137 Slide 25 (Answer) / 137 Express 284,000,000 in Scientific Notation Express 284,000,000 in Scientific Notation 1. Write the number without the comma. 1. Write the number without the comma. 2. 2. Place the decimal so that the first Place the decimal so that the first number will be less than 10 but number will be less than 10 but Answer greater than or equal to 1. greater than or equal to 1. 2.84 x 10 8 3. Count how many places you had 3. Count how many places you had to move the decimal point. This to move the decimal point. This becomes the exponent of 10. becomes the exponent of 10. 4. 4. Drop the zeros to the right of the Drop the zeros to the right of the [This object is a pull tab] right-most non-zero digit. right-most non-zero digit. Slide 26 / 137 Slide 26 (Answer) / 137 5 Which is the correct coefficient of 147,000 when 5 Which is the correct coefficient of 147,000 when it is written in scientific notation? it is written in scientific notation? A 147 A 147 B 14.7 B 14.7 C 1.47 C 1.47 Answer D .147 D .147 C [This object is a pull tab] Slide 27 / 137 Slide 27 (Answer) / 137 6 Which is the correct coefficient of 23,400,000 6 Which is the correct coefficient of 23,400,000 when it is written in scientific notation? when it is written in scientific notation? A .234 A .234 Answer B 2.34 B 2.34 B C 234. C 234. D 23.4 D 23.4 [This object is a pull tab]
Slide 28 / 137 Slide 28 (Answer) / 137 7 How many places do you need to move the 7 How many places do you need to move the decimal point to change 190,000 to 1.9? decimal point to change 190,000 to 1.9? A 3 A 3 Answer B 4 B 4 C C 5 C 5 D 6 D 6 [This object is a pull tab] Slide 29 / 137 Slide 29 (Answer) / 137 8 How many places do you need to move the 8 How many places do you need to move the decimal point to change 765,200,000,000 to 7.652? decimal point to change 765,200,000,000 to 7.652? A 11 A 11 Answer B 10 B 10 A C 9 C 9 D 8 D 8 [This object is a pull tab] Slide 30 / 137 Slide 30 (Answer) / 137 9 Which of the following is 345,000,000 in scientific 9 Which of the following is 345,000,000 in scientific notation? notation? A 3.45 x 10 8 A 3.45 x 10 8 Answer B 3.45 x 10 6 B 3.45 x 10 6 A C 345 x 10 6 C 345 x 10 6 D .345 x 10 9 D .345 x 10 9 [This object is a pull tab]
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