Identify Place are needed to fill the blue block? Values What is - - PDF document

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Decimals

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Define & Review Vocabulary Identify Place Values Read and Write Decimals Compare & Order Decimals Round Numbers to Designated Place Values Relate Fractions, Decimals & Percents Decimal Operations Real Life Applications

Table of Contents Slide 3 / 183

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Define & Review Vocabulary

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A Decimal Number (based

• n the number 10) contains

a Decimal Point. Move me to find out!

What is a decimal number? Slide 5 / 183

What is the value of a yellow rod?

Blue Block Red Block

How many yellow rods are needed to fill the blue block?

Yellow Rod

How many red blocks are needed to fill the blue block? (Hint: Fill a yellow rod with red blocks) What is the value of a red block?

One Unit

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Identify Place Values

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. . . . . . . . . . .

PULL

NOTE: CAN BE STUDEN

Place Value Chart

million hundred thousand ten thousand thousand hundred ten

• n

e a n d tenth hundredth thousandth t e n t h

• u

s a n d t h

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Remember the place values after the decimal point start with tenths

million hundred thousand ten thousand thousand hundred ten

• ne

and tenth hundredth thousandth ten thousandth

9, 8 7 5, 6 1 0 . 4 7 9 4

This number is read: Nine million, eight hundred seventy-five thousand, six hundred ten AND four thousand, seven hundred ninety-four ten thousandths

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1 A 7 What digit is in the thousandths place? 4,567,098.2318 B 1 C 3 D 8

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2 What digit is in the hundreds place? 6,789.043

A

7

B

4

C

3

D

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3 What digit is in the millionths place? 6,754,123.945678

A

6

B

7

C

8

D

4

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4 What digit is in the tens place? 5,432.981

A

4

B

1

C

9

D

3

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5 A 3 B 4 C 2 D 5 What digit is in the ten thousands place? 543,127.9832

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. 7 5 4 6 . 2 5 9 8 . 3 . 8 9 . 1 1 2 3 5 4 . 6 9 . 7 Can you read the number?

thousands hundreds tens

• nes

and tenths h u n d r e d t h s thousandths

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Read & Write Decimals

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• 1. Look to see if there is a number to the left of the

decimal; if so write it out. If there is no number to the left of the decimal, skip to step 3.

• 2. Write an and for the decimal point.
• 3. Write the number in the decimal part.
• 4. Write the word for the place value of the rightmost

digit. How do you write a decimal in words? Write 13.24 in words Thirteen and twenty-four hundredths

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How does a comma help when writing a decimal number? The place value before the comma is always stated. For example: 1,547 is written One THOUSAND, five hundred forty-seven 6,547,100 is written 6 MILLION, five hundred forty-seven THOUSAND,

• ne hundred

Slide 18 / 183 Write the decimal in words

1) 5.04 Five and four hundredths 2) 146.457 One hundred forty-six and four hundred fifty-seven thousandths 3) .0009 Nine ten-thousandths 4) 6,345.1498 Six thousand, three hundred forty-five and one thousand, four hundred ninety-eight ten thousandths

Slide 19 / 183 Writing a decimal numerically

• 1. If there is a ths, there will be a decimal
• 2. If there is an and, there will be a whole number to

the left of the decimal

• 3. Note the ending - this is the place where the

decimal number will end

• 4. Use the decimal chart to help you!

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Use the chart as a guide to write the decimal numbers

• 1. four hundred nineteen and five hundredths
• 2. sixty-five and nine thousandths
• 3. seven thousand, four hundred thirty-three and

twenty hundredths

• 4. six thousand and eight tenths

thousands hundreds tens

• nes

and tenths hundredths thousandths

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Compare & Order Decimals

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Comparing Decimals

· Line up all of the decimal points · Put zeros in wherever digits are missing · Compare the digits, from left to right · The largest digit, having the same place value, names the largest number Example: 910.800 085.007 910.801 911.900 085.070 What digit tells us this is the largest number? 1 Why is this the smallest number? Compare the digits

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Order from least to the greatest

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12.405

Order from least to greatest

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The number with the least value is: A 12.001 B 12.011 C 12.0009 D 12.0019

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7 The number with the least value is: A 0.01 B 0.011 C 0.001 D 0.00101

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The number with the greatest value is: A

2.9 B 2.99 C 2.899 D 2.8999

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9 The number with the greatest value is:

A

597.65

B

598.09

C

598.12

D

597.605

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10 How much money would you like to win? A 1600.50 B 1599.09 C 1601.01 D 1610.02

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Round Numbers to Designated Place Values

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Let's learn how to round decimals using the following examples: Round 513.287 to the nearest tenths place. When rounding decimals, put your pencil point under the place value that you are rounding to DO NOT MOVE IT

513.287

Rounding Decimals Slide 32 / 183

Look to the right. Is the digit 5 or more? Yes OR No What happens to the 2? Increases by 1 OR remains the same What happens to everything to the left of the tenths place? Those digits always remain the same. 513.287 Put your pencil point under the digit in the tenths place. Final Answer: 513.3

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What happened to the digits to the right of the tenths place? Remember, we are rounding. The place values to the right of the tenths place have zero value, so now the digits 8 and 7 become zeroes. 513.300 = 513.3 Try the next example...

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Round 3.14159265 to the nearest hundredths place. First, choose the digit that represents the hundredths place. 11 Answer?

A B C

First, put your pencil point under the 4 and look at the digit to the right. Ask yourself: "Is this digit 5 or more?" Since it's a 1, the 4 remains a 4, and everything after it becomes a zero. 3.14000000 = 3.14

D

Choose which letter is under the hundredths place. 3.14159265

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When rounding to a specific place, your answer MUST have a digit in that place. Example: Round 14.95 to the nearest tenth Answer: 15.0 There must be a digit in the tenths place, since we were to round to the tenths place. Try this: Round 345.6982 to the nearest hundredths place Answer: 345.70

Caution! Slide 36 / 183

12 Round 9876.543219 to the nearest hundredths

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13 Round 9876.543219 to the nearest hundred

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14 Round 9876.543219 to the nearest tenths

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15 Round 9876.543219 to the nearest thousandths

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16 Round 9876.543219 to the nearest unit

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Relate Fractions, Decimals & Percents

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decimals fractions

Writing Decimals as Fractions

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Writing decimals as fractions...

Move the decimal part of the original number into the numerator (without the decimal point) Example 1:

= 0.25 Slide 44 / 183 0.25

Example 1:

=

Then count the number of places to the right

• f the decimal point.

This place value will become your denominator...

25 100 Writing decimals as fractions... Slide 45 / 183

Finally, simplify the fraction.

Writing decimals as fractions...

Example 1:

0.25 = 25 100 = 4 1 Slide 46 / 183 Writing decimals as fractions...

Example 2:

= 0.032

Move the decimal part of the original number into the numerator (without the decimal point)

Slide 47 / 183 0.032

Example 2:

=

Then count the number of places to the right

• f the decimal point.

This place value will become your denominator...

32 1,000 Writing decimals as fractions... Slide 48 / 183

Finally, simplify the fraction.

Writing decimals as fractions...

Example 2:

0.032 = 32 1000 = 125 4

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If there is a whole part to the original number, move the whole part to front of the fraction.

Writing decimals as fractions...

Example 3:

= 4.1

What will the place value be? Move the decimal part of the original number into the numerator (without the decimal point)

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Can this fraction be reduced?

Writing decimals as fractions...

Example 3:

4.1 = 1 10 4 Slide 51 / 183

Let's review how to write a decimal as a fraction! · Numerator is decimal part of the original number · Denominator is place value of rightmost digit · Simplify the fraction · Whole numbers are written in front of the fraction

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17 Write the decimal as a fraction or mixed number in simplest form: 0.85

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18 Write the decimal as a fraction or mixed number in simplest form: 4.375

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19 Write the decimal as a fraction or mixed number in simplest form: 1.0025

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20

Write the decimal as a fraction or mixed number in simplest form: 14.12

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21

Write the decimal as a fraction or mixed number in simplest form: 8.002

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Common Equivalents you should know like the back of your hand!

0.25 0.75 0.5 0.2 1 4 3 4 1 2 1 5 Slide 58 / 183

Some repeating decimals can be converted to fractions. These are common equivalents you should also know!

0.3333... 0.6666... 0.1666... 0.8333... 1 3 2 3 1 6 5 6 Slide 59 / 183

decimals fractions

Writing Fractions as Decimals

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The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit!

Writing fractions as decimals...

Example 1:

7 20 = 7 20

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Then do the math

Writing fractions as decimals...

Example 1:

7 20 = 7.00 20 = 0.35 0.35

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PULL

It is less work to put the 3 in front of the decimal point. What happens if we change the mixed number to an improper fraction? Do we eventually get the same answer?

The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit!

Writing fractions as decimals...

Example 2:

5 8 = 3 5 8 3

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What happens if you use Then do the math

Writing fractions as decimals...

Example 2:

0.625 5 8 = 3 5.000 8 3 = 3.625

29 8 ?

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The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit!

Writing fractions as decimals...

Example 3:

5 6 = 5 6 Slide 65 / 183

Then do the math

Writing fractions as decimals...

Example 3:

5 6 = 5.000 6 0.833 = 0.83 Slide 66 / 183 Definitions:

Repeating decimal: A decimal in which a pattern of

• ne or more digits is repeated indefinitely, such as

0.353535... To show that a decimal is repeating, a bar is often put above the repeating digits: .35 means .353535... A repeating decimal does not end. Terminating decimal: A decimal that has only a finite number of nonzero digits to the right of the decimal point, such as 0.56 Challenge Create a decimal that is non-terminating and non-repeating.

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The Pit! Divide the numerator by the denominator... Or kick the numerator into the pit!

Writing fractions as decimals...

Example 4:

5 3 = 5 3 Slide 68 / 183

Then do the math

Writing fractions as decimals...

Example 4:

5 3 = 5.000 3 1.666 = 1.6

Repeating decimal!

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Then do the math

Writing fractions as decimals...

Example 5:

• 7

4 =

• 7.00

4

• 1.75

= -1.75 Slide 70 / 183

22 Write the fraction as a decimal: 3 10

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23 Write the mixed number as a decimal: 3 4 5

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24 Write the fraction as a decimal: 31 22

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25 Write the fraction as a decimal and round to the nearest hundredth: 3 7

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26

Write the fraction as a decimal:

• 12

5

Slide 75 / 183 1 2 1 3 1 4 0.5 0.3333... 0.25

Common Equivalents you should know like the back of your hand!

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Common Equivalents you should know like the back of your hand!

1 5 2 3 3 4 0.2 0.666... 0.75 Slide 77 / 183

decimals p e r c e n t s

Writing Decimals as Percents

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What does percent mean? Percent means parts per 100 The symbol is % Example: 50% means 50 per 100

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Multiply by 100 and add the percent symbol.

0.75

Example 1:

= 100 0.75 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

0.75 Writing decimals as percents... 75% Slide 80 / 183

Multiply by 100 and add the percent symbol.

0.09

Example 2:

= 100 0.09 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

0.09 Writing decimals as percents... 9%

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Multiply by 100 and add the percent symbol.

0.007

Example 3:

= 100 0.007 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

0.007 Writing decimals as percents... 0.7%

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Multiply by 100 and add the percent symbol.

0.4

Example 4:

= 100 0.4 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

0.4 Writing decimals as percents... 40%

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Multiply by 100 and add the percent symbol.

1.49

Example 5:

= 100 1.49 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

1.49 Writing decimals as percents... 149%

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Multiply by 100 and add the percent symbol.

8

Example 6:

= 100 8 =

Remember To multiply a # by 100, move the decimal two places to the RIGHT.

8 Writing decimals as percents... 800%

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27 Write the decimal as a percent: 0.45 45%

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28 Write the decimal as a percent: 1.3 130%

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29 Write the decimal as a percent: 0.008 .8%

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30 Write the decimal as a percent: 5 500%

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31 Write the decimal as a percent: .2 20%

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percent decimal

Writing Percents as Decimals

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Divide by 100 and remove the percent symbol.

28%

Example 1:

= 100 28% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

28% Writing percents as decimals... 0.28

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Divide by 100 and remove the percent symbol.

8%

Example 2:

= 100 8% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

8% Writing percents as decimals... 0.08

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Divide by 100 and remove the percent symbol.

0.4%

Example 3:

= 100 0.4% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

0.4% Writing percents as decimals... 0.004

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Divide by 100 and remove the percent symbol.

375%

Example 4:

= 100 375% =

Remember To divide a # by 100, move the decimal two places to the LEFT.

375% Writing percents as decimals... 3.75

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32 Write the percent as a decimal: 2% .02

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33 Write the percent as a decimal: 658% 6.58

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34 Write the percent as a decimal: 0.019% .00019

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.043 35 Write the percent as a decimal: 4.3%

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0.005 36 Write the percent as a decimal: .5%

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f r a c t i

• n

s percents

Writing Fractions as Percents

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Write an equivalent fraction with a denominator

• f 100.

Example 1:

3 4 = 100 x 3 4 = 100 x 25 100 75

Writing fractions as percents... 75% 25

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Write an equivalent fraction with a denominator

• f 100.

Example 2:

4 5 = 100 x 4 5 = 100 x 20 100

80 Writing fractions as percents... 80% 20

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Write an equivalent fraction with a denominator

• f 100.

Example3:

9 4 = 100 x 9 4 = 100 x 25 100

225 Writing fractions as percents... 225% 25

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Write an equivalent fraction with a denominator

• f 100.

Example 4:

3

600 = 100 x 3 600 = 100 x 6 100 0.5 Writing fractions as percents... 0.5% 6

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37 Write the fraction as a percent: 19 20 95%

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38 Write the fraction as a percent: 9 1000 .9%

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39 Write the fraction as a percent: 8 100 8%

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40 Write the fraction as a percent: 5 2 250%

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41 Write the fraction as a percent: 3 500 .6%

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To write any fraction as a percent: Express the fraction as a decimal and then express the decimal as a percent. Example 5:

7 8 0.875 7.000 87.5% 8 0.875 100 Slide 111 / 183

To write any fraction as a percent: Express the fraction as a decimal and then express the decimal as a percent. Example 6:

12

9 1.333 12.000 133.3% 9 1.333 100

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To write any fraction as a percent: Express the fraction as a decimal and then express the decimal as a percent. Example 7:

5

8 0.625 5.000 362.5% 8 3.625 100

3 3 Slide 113 / 183

42 Write the fraction as a percent: 5 8 62.5%

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43 Write the fraction as a percent. Round to the nearest whole percent. 4 7 57%

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44 Write the fraction as a percent: 3 5 360% 3

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45 Write the fraction as a percent: 2 500 .4%

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46 Write the fraction as a percent: 9 2 450%

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percents fractions

Writing Percents as Fractions

Slide 119 / 183 Writing percents as fractions...

Express the % as a fraction with a denominator

• f 100, then simplify.

Example 1:

75% = 75 = 100 3 4 Slide 120 / 183 Writing percents as fractions...

Express the % as a fraction with a denominator

• f 100, then simplify.

Example 2:

120% = 120 = 100 1 5 1

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Multiply by 10 to get rid of the decimal

Writing percents as fractions...

Express the % as a fraction with a denominator

• f 100, then simplify.

Example 3:

0.3% = 0.3 = 100 3 1000 Slide 122 / 183

Multiply by 100 to get rid of the decimal

Writing percents as fractions...

Express the % as a fraction with a denominator of 100, then simplify. Example 4: % = = 100 1 4 2 9 4 100 2.25 = 10,000 225 = 400 9

Slide 123 / 183 Writing percents as fractions...another way

Express the % as a fraction with a denominator of 100, then simplify. Example 4: Convert the percent to a fraction. Divide the numerator by the denominator (100). Simplify.

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2 5 47 Write the percent as a fraction in simplest form: 40%

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48 Write the percent as a fraction in simplest form: 110% 11 10

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49 Write the percent as a fraction in simplest form: 0.5% 1 200

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50 Write the percent as a fraction in simplest form: 8% 2 25

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51 Write the percent as a fraction in simplest form: 5 % 4 75

1

3

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Relate Fractions, Decimals & Percents ...Tying it all together!

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Helping you remember... Fill in each box below with an example of the process described. % to a fraction % to a decimal fraction to a % decimal to a %

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52 Find the lowest value A 5% B 1/2 C .5% D .05

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53 Find the greatest value A 120% B 1.02 C .2% D 1.19

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54 Find the greatest value A 6% B .6 C 60 D 6

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55 Find the lowest value A 2% B .2 C .02 D .2%

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56 Find the lowest value A 50% B 500% C 50.0 D 50.01

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Reorder the amount starting with the lowest value

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Reorder the amount starting with the lowest value

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Reorder the amount starting with the lowest value

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Return to Table of Contents

Decimal Operations

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Add decimals 0.25 0.25 0.25 0.25 Four quarters equal one dollar = $1.00

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When adding or subtracting decimals, always remember to align the decimals vertically... 0.25 0.25 0.25 0.25 1.00 +

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Now, try this - Don't forget - LINE 'EM UP 0.1 + 1.25 + 0.04 + 1.39 0.10 1.25 0.04 1.39 + 2.78

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If you know how to add whole numbers then you can add decimals. Just follow these few steps. Step 1: Put the numbers in a vertical column, aligning the decimal points. Step 2: Add each column of digits, starting on the right and working left. Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.

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1.15 57 Add the following: 0.6 + 0.55 A 6.1 B .115 C 1.15 D 0.16

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58 Find the sum 1.025 + 0.03 + 14.0001 15.0551

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59 What is the sum of 12.034 and 0.0104? A 12.1344 B 12.0444 C 12.138 D 1.20444 B

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20.34 60 Find the sum 8 + 0.04 + 12.3 A 13.14 B 19.34 C 20.34 D 20.14

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Find the sum: 5 + 100.14 + 57.89 + 2.3

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Let's go to Cool Math and practice addition: Cool Math Link

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Put the numbers in a vertical column aligning the decimal points. 1.1

• 0.3

Subtract the numbers from right to left using the same rules as whole numbers. 1.1

• 0.3

0.8

Subtract decimals

1

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What do we do if there aren't enough decimal places when we subtract? 4.3 - 2.05 Don't forget...Line 'em Up! 4.3 2.05 What goes here? 4.30 2.05 2.25 2

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Cool Math Link Let's go to Cool Math and practice subtraction:

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5 - 0.23

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12.809 - 4

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1897.11 - 0.647

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4.1 - 0.09

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17 - 13.008

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Multiply & Divide Decimals

To multiply two decimals: · Ignore the decimal points · Multiply the numbers · Count the total number of digits to the right of the decimal points · Put that many digits to the right of the decimal point in your answer

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Multiply & Divide Decimals

3.21 x .04 .1284 There are a total of four digits to the right of the decimal points. There must be four digits to the right

• f the decimal point in the answer.

}

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23.2 x 4.04 928 93.728 There are a total of three digits to the right of the decimal points. There must be three digits to the right of the decimal point in the answer.

}

92800

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67 Multiply 0.4 x 0.03

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68 Multiply 3.45 x 2.1

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69 Multiply 53 x 0.08

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70 Multiply 4.01 x 7.8

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71 Multiply 0.012 x 0.21

Slide 166 / 183 Divide decimals

To divide a decimal by a whole number: Use long division. Bring the decimal point up in the answer 56.08 28 04 2

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Try these! 112.045 56.0008 PULL

Pull

5 2

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To divide a number by a decimal: · Change the divisor to a whole number by multiplying by a power of 10 · Multiply the dividend by the same power of 10 · Divide · Bring the decimal point up in the answer Dividend Divisor

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15.6 6.24 Multiply by 10, so that 15.6 becomes 156 6.24 must also be multiplied by 10 156 62.4 .234 23.4 Multiply by 1000, so that .234 becomes 234 23.4 must also be multiplied by 1000 234 23400

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By what power of 10 should the divisor and dividend be multiplied? 4.15 2.5 means .008 0.9 68.342 means 4.2 678.921 2.2

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72 Divide 0.78 0.02

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73 0.6 4.866

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74 10 divided by 0.25

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75 12.03 0.04

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76 0.012 24.6

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Real Life Applications

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77 If you had six hundredths of a mile left to run, how would you write this distance as a decimal? A 6.0 B .6 C .06 D 06.0 E .60 C

Pull Pull

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78 Your weekly grocery bill averages $97.39. Round your total to the nearest 10 dollars to figure out approximately how much money to save for groceries per week. A $100.00 B $90.00 C $97.00 D $95.00 A

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79 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much did Sally actually make as a profit? A $37.57 B $12.43 C $13.57 D $12.00 B

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80 Five students collected paper to be recycled. Shelly's stack was .008 cm. thick; Ken's stack was .125 cm. thick; Joe's stack was .150 cm. thick; Betty's stack was .185 cm. thick; Mary's stack was .005 cm. thick. What was the thickness of the papers collected to be recycled? A .561 cm. B .452 cm. C .480 cm. D .473 cm. D

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81 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50. What would the total cost be of four pairs of jeans on sale? A $119.96 B $90.00 C $86.00 D $52.49 B

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82 The regular price of a pair of jeans is $29.99.

• Mrs. Jones has four children for whom she must

buy new jeans. The jeans are on sale for $22.50. How much money does she save by buying the jeans on sale? A $7.49 B $30.96 C $29.96 D $89.96 C

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