Expressing Fractions as Decimals

Sometimes we will want to work with decimals instead of fractions. To convert fractions to decimals, simply divide the numerator by the denominator, either using a calculator or by hand using the usual method of long division. When using long division, don't leave the remainder as a whole number. Instead, treat the numerator as a decimal with zeroes after the decimal point (for example, treat 56 as 56.000). Continue to divide, making sure the decimal point is in the same place in the numerator and the answer.

Example 3. Convert 7/4 into a decimal.

By calculator: 7/4 = 1.75
By long division: 7/4 = 7.00/4 = 1.75

Terminating and Repeating Decimals

Try to change 1/3 into a decimal on a calculator. The answer should be 0.3333333.... Similarly, 5/12 = 0.416666666... and 13/99 = 0.13131313...

Decimals that endlessly repeat one number or a group of numbers are called repeating decimals. The part that repeats is usually written as a single number (or group of numbers) with a line over it. For example, 0.3333333..., 0.4166666..., and 0.13131313... are written as 0., 0.41, 0.,
Decimals that stop after a certain place are called terminating decimals. Every fraction can be written as either a terminating decimal or a repeating decimal.

Example 4. Do the following fractions convert to terminating or repeating decimals? 4/6, 9/6, 109/99, 5/4.

4/6. Repeating
9/6. Terminating
109/99. Repeating
5/4. Terminating