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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
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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
Return to Table of Contents
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
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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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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
Return to Table of Contents
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!
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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
thou
sand
s
hund
reds
tens
ones
and
tent
hs
hund
redt
hs
thou
sand
ths
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Return to Table of Contents
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
Slide 28 / 183
10 How much money would you like to win?
A 1600.50
B 1599.09
C 1601.01
D 1610.02
Slide 29 / 183
Return to Table of Contents
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
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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!
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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
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16 Round
9876.543219
to the nearest unit
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Return to Table of Contents
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 43 / 183
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
Writing decimals as fractions...
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Finally, simplify the fraction.
Writing decimals as fractions...
Example 1:
0.25 =25
100=
4
1
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Writing decimals as fractions...
Example 2:
=0.032
Move the decimal part of the original number into the numerator (without the decimal point)
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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
Writing decimals as fractions...
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Finally, simplify the fraction.
Writing decimals as fractions...
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.
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
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
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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
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
Writing fractions as decimals...
Example 1:
7
20=
7.0020=0.35 0.35
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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!
Divide the numerator by the denominator...Or kick the numerator into the pit!
Writing fractions as decimals...
Example 2:
5
8=3
5
83
Slide 62 / 183
What happens if you use
Then do the math
Writing fractions as decimals...
Example 2:
0.6255
8=3
5.00083 = 3.625
298
?
Slide 63 / 183
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 64 / 183
Then do the math
Writing fractions as decimals...
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.
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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 67 / 183
Then do the math
Writing fractions as decimals...
Example 4:
5
3=
5.00031.666
= 1.6
Repeatingdecimal!
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Then do the math
Writing fractions as decimals...
Example 5:
-74
=-7.004-1.75
= -1.75
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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
24 Write the fraction as a decimal:
31 22
Slide 72 / 183
25 Write the fraction as a decimal and round to the nearest hundredth:
37
Slide 73 / 183
26 Write the fraction as a decimal:
-12
5
Slide 74 / 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
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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
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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%
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Multiply by 100 and add the percent symbol.
0.09
Example 2:
=1000.09 =
RememberTo multiply a # by 100, move the decimal two places to the RIGHT. 0.09
Writing decimals as percents...
9%
Slide 80 / 183
Multiply by 100 and add the percent symbol.
0.007
Example 3:
=1000.007 =
RememberTo multiply a # by 100, move the decimal two places to the RIGHT. 0.007
Writing decimals as percents...
0.7%
Slide 81 / 183
Multiply by 100 and add the percent symbol.
0.4
Example 4:
=1000.4 =
RememberTo multiply a # by 100, move the decimal two places to the RIGHT. 0.4
Writing decimals as percents...
40%
Slide 82 / 183
Multiply by 100 and add the percent symbol.
1.49
Example 5:
=1001.49 =
RememberTo 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:
=1008 =
RememberTo 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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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
Divide by 100 and remove the percent symbol.
8%
Example 2:
=1008% =
RememberTo 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:
=1000.4% =
RememberTo divide a # by 100, move the decimal two places to the LEFT. 0.4%
Writing percents as decimals...
0.004
Slide 93 / 183
Divide by 100 and remove the percent symbol.
375%
Example 4:
=100375% =
RememberTo 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
Slide 95 / 183
33 Write the percent as a decimal:
658%
6.58
Slide 96 / 183
34 Write the percent as a decimal:
0.019%
.00019
Slide 97 / 183
.043
35 Write the percent as a decimal:
4.3%
Slide 98 / 183
0.005
36 Write the percent as a decimal:
.5%
Slide 99 / 183
fractions
percents
Writing Fractions as Percents
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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
Write an equivalent fraction with a denominator of 100.
Example 2:
45
=100
x 45
=100
x20
10080
Writing fractions as percents...
80%
20
Slide 102 / 183
Write an equivalent fraction with a denominator of 100.
Example3:
94
=100
x 94
=100
x25
100225
Writing fractions as percents...
225%
25
Slide 103 / 183
Write an equivalent fraction with a denominator of 100.
Example 4:
3600
=100
x 3600
=100
x6
1000.5
Writing fractions as percents...
0.5%
6
Slide 104 / 183
37 Write the fraction as a percent:
1920
95%
Slide 105 / 183
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%
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
To write any fraction as a percent:
Express the fraction as a decimaland then express the decimal as a percent.
Example 6:
129
1.33312.000
133.3%
91.333 100
Slide 111 / 183
To write any fraction as a percent:
Express the fraction as a decimaland then express the decimal as a percent.
Example 7:
58
0.6255.000
362.5%
83.625 1003 3
Slide 112 / 183
42 Write the fraction as a percent:
58
62.5%
Slide 113 / 183
43 Write the fraction as a percent. Round to the nearest whole percent.
47
57%
Slide 114 / 183
44 Write the fraction as a percent:
3 5
360%
3
Slide 115 / 183
45 Write the fraction as a percent:
2 500
.4%
Slide 116 / 183
46 Write the fraction as a percent:
92
450%
Slide 117 / 183
percents
fractions
Writing Percents as Fractions
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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
Writing percents as fractions...
Express the % as a fraction with a denominator of 100, then simplify.
Example 2:
120% =120
=100
1
51
Slide 120 / 183
Multiply by 10to get rid of the decimal
Writing percents as fractions...
Express the % as a fraction with a denominator of 100, then simplify.
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%
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48 Write the percent as a fraction in simplest form:
110%
1110
Slide 125 / 183
49 Write the percent as a fraction in simplest form:
0.5%
1200
Slide 126 / 183
50 Write the percent as a fraction in simplest form:
8%
2 25
Slide 127 / 183
51 Write the percent as a fraction in simplest form:
5 %
4 75
13
Slide 128 / 183
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 %
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
55 Find the lowest value
A 2%
B .2
C .02
D .2%
Slide 134 / 183
56 Find the lowest value
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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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
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+
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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
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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
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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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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
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
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
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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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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
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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
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73
0.6 4.866
Slide 172 / 183
74
10 divided by 0.25
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75
12.03 0.04
Slide 174 / 183
76
0.012 24.6
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Real Life Applications
Return to Table of Contents
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
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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
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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 $12.00B
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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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