4-4 Decimals and Fractions Learn to convert between decimals and fractions.
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Transcript of 4-4 Decimals and Fractions Learn to convert between decimals and fractions.
4-4 Decimals and Fractions
A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number.
34
__
__41
1 1__21
1 __43
2 __41
2 __21
Mixed numbers12
14
34
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5
4-4 Decimals and Fractions
Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers
Write each decimal as a fraction or mixed number.
0.67
Identify the place value of the digit farthest to the right.
The 7 is in the hundredths place, so use 100 as the denominator.
0.67
100____67 Remember!
One
s
Ten
ths
Hun
dred
ths
Tho
usan
dths
Place Value
4-4 Decimals and Fractions
Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers
Write each decimal as a fraction or mixed number.
5.9
Identify the place value of the digit farthest to the right.Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator.
5.9
10 ___ 9
5
4-4 Decimals and Fractions
Check It Out: Example 1A
Write each decimal as a fraction or mixed number.
0.73
Identify the place value of the digit farthest to the right.
The 3 is in the hundredths place, so use 100 as the denominator.
0.73
100____73
4-4 Decimals and Fractions
Check It Out: Example 1B
Write each decimal as a fraction or mixed number.
4.8
Identify the place value of the digit farthest to the right.Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator.
4.8
10 ___ 8
4
4-4 Decimals and Fractions
Additional Example 2A: Writing Fractions as Decimals
Write each fraction or mixed number as a decimal.
Divide 3 by 20.
Add zeros after the decimal point.
0 20____ 3
The remainder is 0.
.00- 20
.1320
100- 100
5
0
20____ 3
= 0.15
4-4 Decimals and Fractions
To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6
Writing Math
4-4 Decimals and Fractions
Additional Example 2B: Writing Fractions as Decimals
Divide 1 by 3.
Add zeros after the decimal point.
0 3 __ 1
The 3 repeats in the quotient.
.000- 9
.31 3
10- 9
3
10
=
6
- 9
3
1 3 __ 1
6 6.333… = 6.3_
Write each fraction or mixed number as a decimal.
4-4 Decimals and Fractions
Check It Out: Example 2A
Write each fraction or mixed number as a decimal.
Divide 5 by 20.
Add zeros after the decimal point.
0
20____ 5
The remainder is 0.
.00- 40
.25 20
100- 100
5
0
20____ 5
= 0.25
4-4 Decimals and Fractions
Check It Out: Example 2B
Write each fraction or mixed number as a decimal.
Divide 2 by 3.
Add zeros after the decimal point.
0
3 __ 2
The 6 repeats in the quotient.
.000- 18
.62 3
20- 18
6
20
=
7
- 18
6
2 3 __ 2
7 7.666… = 7.6_
4-4 Decimals and Fractions
A terminating decimal, such as 0.75, has a finite number of decimal places. A repeating decimal, such as 0.666…, has a block of one or more digits that repeat continuously
0.80.750.60.60.50.40.30.250.2
Common Fractions and Equivalent Decimals1
3__1
5__ 1
4__ 2
5__ 1
2__ 3
5__ 2
3__ 3
4__ 4
5__
4-4 Decimals and Fractions
Additional Example 3: Comparing and Ordering Fractions and Decimals
Order the fractions and decimals from least to greatest.
, 0.8, 7 __10
3__4
First rewrite the fractions as decimals. = 0.75 = 0.7
Order the three decimals.
3 __ 4
0
7 __10
__107
3 __ 4
0.75 0.80.7
The numbers in order from least to greatest are , , and 0.8. 710
3 4
4-4 Decimals and Fractions
Check It Out: Example 3
Order the fractions and decimals from least to greatest.
, 0.35, 1 __ 4
1__2
First rewrite the fractions as decimals. = 0.5 = 0.25
Order the three decimals.
1 __ 2
0
1 __ 4
1__ 2
The numbers in order from least to greatest are , 0.35, and . 1 __ 4
1 __ 2
0.35 0.50.25
1 __ 4