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**4.4 Decimals and Fractions**

I can convert between decimals and fractions.

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**Write the day of the month as the product of two factors.**

Review of Factors Write the day of the month as the product of two factors. Possible answer: 12th of the month, 6 2

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Vocabulary mixed number terminating decimal repeating decimal

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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

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**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

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**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.

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**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

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**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 =

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**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 __

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**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 = = 0.7 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

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