Learn to convert between decimals and fractions. 1

Vocabulary mixed number terminating decimal repeating decimal 2

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 1 4 1 2 3 4 __ 4 1 1 __ 2 1 __ 4 3 2 __ 4 1 2 __ 1 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 3

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. 100 ____ 67 The 7 is in the hundredths place, so use 100 as the denominator. Remember! Ones Tenths Hundredths Thousandths Place Value 4

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. 10 ___ 9 5 Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator. 5

Write each decimal as a fraction or mixed number. 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. 100 ____ 73 The 3 is in the hundredths place, so use 100 as the denominator. 6

Write each decimal as a fraction or mixed number. 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. 10 ___ 8 4 Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator. 7

Additional Example 2A: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 20 ____ 3 .1 5 Divide 3 by 20. 20 3 .00 Add zeros after the decimal point. - 20 100 - 100 The remainder is 0. 20 ____ 3 = 0.15 8

Writing Math To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6 9

Additional Example 2B: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 3 __ 1 6 .3 3 3 Divide 1 by 3. 3 1 .000 Add zeros after the decimal point. - 9 10 The 3 repeats in the quotient. - 9 10 - 9 6.333… = 6.3 _ 1 3 __ 1 6 = 10

Write each fraction or mixed number as a decimal. Check It Out: Example 2A Write each fraction or mixed number as a decimal. 20 ____ 5 .2 5 Divide 5 by 20. 20 5 .00 Add zeros after the decimal point. - 40 100 - 100 The remainder is 0. 20 ____ 5 = 0.25 11

Write each fraction or mixed number as a decimal. Check It Out: Example 2B Write each fraction or mixed number as a decimal. 3 __ 2 7 .6 6 6 Divide 2 by 3. 3 2 .000 Add zeros after the decimal point. - 18 20 The 6 repeats in the quotient. - 18 20 - 18 7.666… = 7.6 _ 2 3 __ 2 7 = 12

Common Fractions and Equivalent Decimals 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 0.8 0.75 0.6 0.5 0.4 0.3 0.25 0.2 Common Fractions and Equivalent Decimals 1 5 __ 1 4 __ 1 3 __ 2 5 __ 1 2 __ 3 5 __ 2 3 __ 3 4 __ 4 5 __ 13

Additional Example 3: Comparing and Ordering Fractions and Decimals Order the fractions and decimals from least to greatest. __ 3 __ 7 , 0.8, 4 10 3 __ 4 __ 10 7 First rewrite the fractions as decimals. = 0.75 = 0.7 Order the three decimals. 7 __ 10 3 __ 4 0.7 0.75 0.8 The numbers in order from least to greatest are , , and 0.8. 7 10 3 4 14

Order the fractions and decimals from least to greatest. Check It Out: Example 3 Order the fractions and decimals from least to greatest. 1 1 __ 4 , 0.35, __ 2 1 __ 2 1 __ 4 First rewrite the fractions as decimals. = 0.5 = 0.25 Order the three decimals. 1 __ 4 1 __ 2 0.25 0.35 0.5 1 __ 4 1 __ The numbers in order from least to greatest are , 0.35, and . 2 15