Decimals - NJCTLcontent.njctl.org/courses/math/archived-coursesunits-prior-to... · Decimals Slide 1 / 183 Define & Review Vocabulary Identify Place Values Read and Write Decimals

Decimals

Slide 1 / 183

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 2 / 183

Return to Table of Contents

Define & Review Vocabulary

Slide 3 / 183

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A Decimal Number (based on the number 10) contains

a Decimal Point.

Move me to find out!

What is a decimal number?

Slide 4 / 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

Slide 5 / 183


Identify Place Values

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.

.

.

.

.

.

.

.

.

.

.

PULLNOTE: CAN BESTUDEN

Place Value Chart

mill

ion

hund

red

thou

sand

ten

thou

sand

thou

sand

hund

red

ten

one

and

tent

h

hund

redt

h

thou

sand

thte

n th

ousa

ndth

Slide 7 / 183

Remember the place values after the decimal point start with tenths

mill

ion

hund

red

thou

sand

ten

thou

sand

thou

sand

hund

red

ten

one

and

tent

h

hund

redt

h

thou

sand

thte

n th

ousa

ndth

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

Slide 8 / 183

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 0

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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

Slide 12 / 183

5

A 3

B 4

C 2

D 5

What digit is in the ten thousands place?

543,127.9832

Slide 13 / 183

0 . 0 7

5 4 6 . 2 5 9

8 . 3

0 . 8 9

0 . 0 1 1

2 3 5 4 . 6

9 . 7

Can you read the number?

thou

sand

s

hund

reds

tens

ones

and

tent

hs

hund

redt

hs

thou

sand

ths

Slide 14 / 183


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

Slide 16 / 183

How does a comma help when writing a decimal number?

The place value before the comma is always stated.

For example:

1,547 is writtenOne THOUSAND, five hundred forty-seven

6,547,100 is written6 MILLION, five hundred forty-seven THOUSAND, one hundred

Slide 17 / 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 18 / 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!

Slide 19 / 183

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

thou

sand

s

hund

reds

tens

ones

and

tent

hs

hund

redt

hs

thou

sand

ths

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Compare & OrderDecimals

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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:

910.800085.007910.801911.900085.070

What digit tells us this is the largest number?

1

Why isthis the smallest number?

Compare the digits

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Order from least to the greatest

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12.405Order from least to greatest

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6 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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8 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

Slide 29 / 183


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 31 / 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

Slide 32 / 183

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...

Slide 33 / 183

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

Slide 34 / 183

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!

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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

Slide 39 / 183

16 Round

9876.543219

to the nearest unit

Slide 40 / 183



Slide 41 / 183

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

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0.25

Example 1:

=

Then count the number of places to the right of the decimal point.

This place value will become your denominator...

25

100


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Finally, simplify the fraction.


Example 1:

0.25 =25

100=

4

1

Slide 45 / 183


Example 2:

=0.032


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0.032

Example 2:

=

Then count the number of places to the right of the decimal point.

This place value will become your denominator...

32

1,000


Slide 47 / 183

Finally, simplify the fraction.


Example 2:

0.032 =32

1000=

125

4

Slide 48 / 183

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


Example 3:

=4.1

What will the place value be?


Slide 49 / 183

Can this fraction be reduced?


Example 3:

4.1 =1

104

Slide 50 / 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

Slide 51 / 183

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

0.85

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4.375

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1.0025

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

Slide 55 / 183


8.002

Slide 56 / 183

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

0.25 0.75 0.5 0.2

14

34

12

15

Slide 57 / 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...

13

23

16

56

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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

Slide 60 / 183

Then do the math


Example 1:

7

20=

7.0020=0.35 0.35

Slide 61 / 183

PULLIt 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!



Example 2:

5

8=3

5

83

Slide 62 / 183

What happens if you use

Then do the math


Example 2:

0.6255

8=3

5.00083 = 3.625

298

?

Slide 63 / 183

The Pit!



Example 3:

5

6=

5

6

Slide 64 / 183

Then do the math


Example 3:

5

6=

5.00060.833

= 0.83

Slide 65 / 183

Definitions:Repeating decimal: A decimal in which a pattern of one 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.

Slide 66 / 183

The Pit!



Example 4:

5

3=

5

3

Slide 67 / 183

Then do the math


Example 4:

5

3=

5.00031.666

= 1.6

Repeatingdecimal!

Slide 68 / 183

Then do the math


Example 5:

-74

=-7.004-1.75

= -1.75

Slide 69 / 183

22 Write the fraction as a decimal:

3 10

Slide 70 / 183

23 Write the mixed number as a decimal: 3

4

5

Slide 71 / 183


31 22

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

37

Slide 73 / 183


-12

5

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1 2

1 3

1 4

0.5 0.3333... 0.25


Slide 75 / 183


1 5

2 3

3 4

0.2 0.666... 0.75

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0

deci

mal

s percents

Writing Decimals as Percents

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What does percent mean?

Percent means parts per 100The symbol is %

Example: 50% means 50 per 100

Slide 78 / 183

Multiply by 100 and add the percent symbol.

0.75

Example 1:

=1000.75 =

RememberTo multiply a # by 100, move the decimal two places to the RIGHT. 0.75

Writing decimals as percents...

75%

Slide 79 / 183


0.09

Example 2:

=1000.09 =



9%

Slide 80 / 183


0.007

Example 3:

=1000.007 =



0.7%

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0.4

Example 4:

=1000.4 =



40%

Slide 82 / 183


1.49

Example 5:

=1001.49 =



149%

Slide 83 / 183


8

Example 6:

=1008 =

RememberTo multiply a # by 100, move the decimal two places to the RIGHT. 8


800%

Slide 84 / 183

27 Write the decimal as a percent:

0.45

45%

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1.3

130%

Slide 86 / 183


0.008

.8%

Slide 87 / 183


5

500%

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.2

20%

Slide 89 / 183

perc

ent

decimal

Writing Percents as Decimals

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Divide by 100 and remove the percent symbol.

28%

Example 1:

=10028% =

RememberTo divide a # by 100, move the decimal two places to the LEFT. 28%

Writing percents as decimals...

0.28

Slide 91 / 183


8%

Example 2:

=1008% =



0.08

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0.4%

Example 3:

=1000.4% =

RememberTo divide a # by 100, move the decimal two places to the LEFT. 0.4%


0.004

Slide 93 / 183


375%

Example 4:

=100375% =



3.75

Slide 94 / 183

32 Write the percent as a decimal:

2%

.02

Slide 95 / 183


658%

6.58

Slide 96 / 183


0.019%

.00019

Slide 97 / 183

.043


4.3%

Slide 98 / 183

0.005


.5%

Slide 99 / 183

fractions

percents

Writing Fractions as Percents

Slide 100 / 183

Write an equivalent fraction with a denominator of 100.

Example 1:

34

=100

x 34

=100

x25

10075

Writing fractions as percents...

75%

25

Slide 101 / 183


Example 2:

45

=100

x 45

=100

x20

10080


80%

20

Slide 102 / 183


Example3:

94

=100

x 94

=100

x25

100225


225%

25

Slide 103 / 183


Example 4:

3600

=100

x 3600

=100

x6

1000.5


0.5%

6

Slide 104 / 183

37 Write the fraction as a percent:

1920

95%

Slide 105 / 183


9 1000

.9%

Slide 106 / 183


8 100

8%

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5 2

250%

Slide 108 / 183


3 500

.6%

Slide 109 / 183

To write any fraction as a percent:

Express the fraction as a decimaland then express the decimal as a percent.

Example 5:

78

0.8757.000

87.5%

80.875 100

Slide 110 / 183



Example 6:

129

1.33312.000

133.3%

91.333 100

Slide 111 / 183



Example 7:

58

0.6255.000

362.5%

83.625 1003 3

Slide 112 / 183


58

62.5%

Slide 113 / 183

43 Write the fraction as a percent. Round to the nearest whole percent.

47

57%

Slide 114 / 183


3 5

360%

3

Slide 115 / 183


2 500

.4%

Slide 116 / 183


92

450%

Slide 117 / 183

percents

fractions

Writing Percents as Fractions

Slide 118 / 183

Writing percents as fractions...

Express the % as a fraction with a denominator of 100, then simplify.

Example 1:

75% =75

=100

3

4

Slide 119 / 183



Example 2:

120% =120

=100

1

51

Slide 120 / 183

Multiply by 10to get rid of the decimal



Example 3:

0.3% =0.3

=100

3

1000

Slide 121 / 183

Multiply by 100to 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

42

9

4

100

2.25=

10,000

225=

400

9

Slide 122 / 183

Writing percents as fractions...another wayExpress 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.

Slide 123 / 183

2 5

47 Write the percent as a fraction in simplest form:

40%

Slide 124 / 183


110%

1110

Slide 125 / 183


0.5%

1200

Slide 126 / 183


8%

2 25

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5 %

4 75

13

Slide 128 / 183


...Tying it all together!

Slide 129 / 183

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 %

Slide 130 / 183

52 Find the lowest value

A 5%

B 1/2

C .5%

D .05

Slide 131 / 183

53 Find the greatest value

A 120%

B 1.02

C .2%

D 1.19

Slide 132 / 183

54 Find the greatest value

A 6%

B .6

C 60

D 6

Slide 133 / 183


A 2%

B .2

C .02

D .2%

Slide 134 / 183


A 50%

B 500%

C 50.0

D 50.01

Slide 135 / 183

Reorder the amount starting with the lowest value

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Decimal Operations

Slide 139 / 183

Add decimals

0.25 0.25 0.25 0.25

Four quarters equal one dollar

= $1.00

Slide 140 / 183

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

0.250.250.250.251.00+

Slide 141 / 183

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Now, try this - Don't forget - LINE 'EM UP

0.1 + 1.25 + 0.04 + 1.39

0.101.250.041.39+

2.78

Slide 142 / 183

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.

Slide 143 / 183

1.15

57 Add the following:

0.6 + 0.55

A 6.1

B .115

C 1.15

D 0.16

Slide 144 / 183

58 Find the sum

1.025 + 0.03 + 14.0001

15.0551

Slide 145 / 183

59 What is the sum of

12.034 and 0.0104?

A 12.1344

B 12.0444

C 12.138

D 1.20444

B

Slide 146 / 183

20.34

60 Find the sum

8 + 0.04 + 12.3

A 13.14

B 19.34

C 20.34

D 20.14

Slide 147 / 183

61 Find the sum:

5 + 100.14 + 57.89 + 2.3

Slide 148 / 183

Let's go to Cool Math and practice addition:

Cool Math Link

Slide 149 / 183

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

10

Slide 150 / 183

http://www.coolmath.com/prealgebra/02-decimals/decimals-cruncher-addition.html

What do we do if there aren't enough decimal places when we subtract?

4.3 - 2.05

Don't forget...Line 'em Up!

4.32.05

What goes here?

4.302.05

2.25

2

Slide 151 / 183

Cool Math Link

Let's go to Cool Math and practice subtraction:

Slide 152 / 183

625 - 0.23

Slide 153 / 183

http://www.coolmath.com/prealgebra/02-decimals/decimals-cruncher-subtraction.htm

6312.809 - 4

Slide 154 / 183

641897.11 - 0.647

Slide 155 / 183

654.1 - 0.09

Slide 156 / 183

6617 - 13.008

Slide 157 / 183

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

Slide 158 / 183

Multiply & Divide Decimals

3.21x .04

.1284

There are a total of four digits to the right of the decimal points.

There must be four digits to the right of the decimal point in the answer.

}

Slide 159 / 183

23.2x 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

Slide 160 / 183

67 Multiply 0.4 x 0.03

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69 Multiply 53 x 0.08

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71 Multiply 0.012 x 0.21

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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

Slide 166 / 183

Try these!

112.045

56.0008

PULLPull5

2

Slide 167 / 183

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

DividendDivisor

Slide 168 / 183

15.6 6.24

Multiply by 10, so that 15.6 becomes 1566.24 must also be multiplied by 10

156 62.4

.234 23.4

Multiply by 1000, so that .234 becomes 23423.4 must also be multiplied by 1000

234 23400

Slide 169 / 183

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

Slide 170 / 183

72 Divide

0.78 0.02

Slide 171 / 183

73

0.6 4.866

Slide 172 / 183

74

10 divided by 0.25

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75

12.03 0.04

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76

0.012 24.6

Slide 175 / 183

Real Life Applications


Slide 176 / 183

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

Slide 177 / 183

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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 $95.00A

Slide 178 / 183

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 $12.00B

Slide 179 / 183

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

Slide 180 / 183

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

Slide 181 / 183

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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Slide 183 / 183

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Decimals - NJCTLcontent.njctl.org/courses/math/archived-coursesunits-prior-to... · Decimals Slide 1 / 183 Define & Review Vocabulary Identify Place Values Read and Write Decimals