Transcript Document
4-4 Decimals and Fractions Learn to convert between decimals and fractions. 4-4 Decimals and Fractions Vocabulary mixed number terminating decimal repeating decimal 4-4 Decimals and Fractions A number that contains both a whole number greater than 0 and a fraction, 3 __ such as 1 4 , is called a mixed number. 1 4 0 0.25 1 2 Mixed numbers 1 1 3 1 1 __ __ 1__ 1 __ 1 __ 2 2 4 2 4 4 2 3 4 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 0.67 Identify the place value of the digit farthest to the right. Remember! Thousandths Hundredths Place Value Tenths 100 The 7 is in the hundredths place, so use 100 as the denominator. Ones 67 ____ 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 5.9 Identify the place value of the digit farthest to the right. 9 5 ___ Write the whole number, 5. The 9 is in the tenths 10 place, so use 10 as the denominator. 4-4 Decimals and Fractions 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. 73 ____ 100 The 3 is in the hundredths place, so use 100 as the denominator. 4-4 Decimals and Fractions 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. 8 4 ___ Write the whole number, 4. The 8 is in the tenths 10 place, so use 10 as the denominator. 4-4 Decimals and Fractions Additional Example 2A: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 3 ____ 20 0.15 20 3 .00 - 20 100 - 100 0 Divide 3 by 20. Add zeros after the decimal point. The remainder is 0. 3 ____ = 0.15 20 4-4 Decimals and Fractions Writing Math To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6 4-4 Decimals and Fractions Additional Example 2B: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 6 1 __ 3 0.333 3 1 .000 -9 10 -9 10 -9 1 Divide 1 by 3. Add zeros after the decimal point. The 3 repeats in the quotient. 6 1 __ 3 _ = 6.333… = 6.3 4-4 Decimals and Fractions Check It Out: Example 2A Write each fraction or mixed number as a decimal. 5 ____ 20 0.25 20 5 .00 - 40 100 - 100 0 Divide 5 by 20. Add zeros after the decimal point. The remainder is 0. 5 ____ = 0.25 20 4-4 Decimals and Fractions Check It Out: Example 2B Write each fraction or mixed number as a decimal. 7 2 __ 3 0.666 3 2 .000 - 18 20 - 18 20 - 18 2 Divide 2 by 3. Add zeros after the decimal point. The 6 repeats in the quotient. 7 2 __ 3 _ = 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 Common Fractions and Equivalent Decimals 1 __ 1 __ 1 __ 1 __ 5 2 __ 3 __ 4 3 5 2 0.4 0.5 0.2 0.25 0.3 2 __ 3 __ 5 3 4 __ 4 5 0.6 0.6 0.75 0.8 4-4 Decimals and Fractions Additional Example 3: Comparing and Ordering Fractions and Decimals Order the fractions and decimals from least to greatest. 3 7 __ , 0.8, __ 10 4 3 7 First rewrite the fractions as decimals. __ = 0.75 __ = 0.7 10 4 Order the three decimals. 7 __ 10 0 3 __ 4 0.7 0.75 0.8 The numbers in order from least to greatest are 7 , 3 , and 0.8. 10 4 4-4 Decimals and Fractions Check It Out: Example 3 Order the fractions and decimals from least to greatest. 1 1 , 0.35, __ __ 4 2 1 1 First rewrite the fractions as decimals. __ = 0.5 __ = 0.25 2 4 Order the three decimals. 1 1 __ __ 4 2 0 0.25 0.35 0.5 1 1 The numbers in order from least to greatest are __ , 0.35, and __ . 2 4