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Learn to convert between decimals and fractions. Vocabulary. mixed number terminating decimal repeating decimal. 1. 1. 3. 1. 1. __. __. __. __. __. 1. 1. 1. 2. 2. 4. 2. 4. 4. 2. 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5.
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Vocabulary mixed number terminating decimal repeating decimal
1 1 3 1 1 __ __ __ __ __ 1 1 1 2 2 4 2 4 4 2 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number. 3 __ 4 Mixed numbers 12 34 14
67 ____ Remember! 100 Place Value Hundredths Thousandths Ones Tenths Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 0.67 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.
9 ___ 10 Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 5.9 5.9 Identify the place value of the digit farthest to the right. 5 Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator.
73 ____ 100 Check It Out: Example 1A Write each decimal as a fraction or mixed number. 0.73 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.
8 ___ 10 Check It Out: Example 1B Write each decimal as a fraction or mixed number. 4.8 4.8 Identify the place value of the digit farthest to the right. 4 Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator.
3 ____ 20 3 ____ 20 Additional Example 2A: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 0 .1 5 Divide 3 by 20. 20 3 .00 Add zeros after the decimal point. - 20 100 - 100 The remainder is 0. 0 = 0.15
Writing Math To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6
1 __ 3 _ 1 __ 6.333… = 6.3 3 Additional Example 2B: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 6 0 .3 3 3 Divide 1 by 3. .000 3 1 Add zeros after the decimal point. - 9 10 The 3 repeats in the quotient. - 9 10 - 9 1 6 =
5 ____ 20 5 ____ 20 Check It Out: Example 2A Write each fraction or mixed number as a decimal. 0 .2 5 Divide 5 by 20. .00 20 5 Add zeros after the decimal point. - 40 100 - 100 The remainder is 0. 0 = 0.25
2 __ 3 _ 2 __ 7.666… = 7.6 3 Check It Out: Example 2B Write each fraction or mixed number as a decimal. 7 0 .6 6 6 Divide 2 by 3. .000 3 2 Add zeros after the decimal point. - 18 20 The 6 repeats in the quotient. - 18 20 - 18 2 7 =
Common Fractions and Equivalent Decimals 1 2 1 1 1 3 2 3 4 __ __ __ __ __ __ __ __ __ 5 3 4 3 2 4 5 5 5 0.2 0.25 0.3 0.4 0.5 0.6 0.6 0.75 0.8 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
3 __ __ 10 4 7 3 __ __ 10 4 3 7 The numbers in order from least to greatest are , , and 0.8. 4 10 Additional Example 3: Comparing and Ordering Fractions and Decimals Order the fractions and decimals from least to greatest. 3 7 __ __ , 0.8, 10 4 7 First rewrite the fractions as decimals. = 0.75 = 0.7 Order the three decimals. 0 0.8 0.75 0.7
1 __ 4 1 1 __ __ 2 4 1 1 __ __ 4 2 1 __ 4 Check It Out: Example 3 Order the fractions and decimals from least to greatest. 1 __ , 0.35, 2 First rewrite the fractions as decimals. = 0.5 = 0.25 Order the three decimals. 0 0.35 0.5 0.25 1 __ The numbers in order from least to greatest are , 0.35, and . 2
