9 Decimals that terminate or repeat are rational numbers. To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.
10 Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form.A. 5.3737 100= 55.377 is in the hundredths place.B=2 is in the thousandths place.0.622Simplify by dividing by the common factor 2.=
11 = 8 = 8 = = 75 100 8.75 5 is in the hundredths place. Check It Out: Example 2Write each decimal as a fraction in simplest form.A. 8.7575 100= 88.755 is in the hundredths place.Simplify by dividing by the common factor 25.= 83 4B,000=5 is in the ten-thousandths place.0.2625=21 80Simplify by dividing by the common factor 125.
12 Additional Example 3A: Writing Fractions as Decimals Write the fraction as a decimal.11 91.29 11.0The pattern repeats.–92–18A repeating decimal can be written with a bar over the digits that repeat. So … = 1.2.Writing Math_2The fraction is equivalent to the decimal 1.2.11 9
13 Additional Example 3B: Writing Fractions as Decimals Write the fraction as a decimal.7 20.35This is a terminating decimal.20 7.0–07–6 01 0–1 0The remainder is 0.The fraction is equivalent to the decimal 0.35.7 20
14 The fraction is equivalent to the decimal 1.6. 15 9 Check It Out: Example 3AWrite the fraction as a decimal.15 91.69 15.0The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal.–96–546The fraction is equivalent to the decimal 1.6.15 9