Converting Fractions to Decimals
Learning Outcomes
- Convert a fraction to a decimal
- Identify a fraction whose decimal form is repeating
- Add a fraction and decimal by converting between forms
Convert a Fraction to a Decimal
To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.example
Write the fraction as a decimal. SolutionA fraction bar means division, so we can write the fraction using division. | ![]() |
Divide. | ![]() |
So the fraction is equal to . |
try it
[ohm_question]146253[/ohm_question]example
Write the fraction as a decimal.Answer: Solution
The value of this fraction is negative. After dividing, the value of the decimal will be negative. We do the division ignoring the sign, and then write the negative sign in the answer. | |
Divide by . | ![]() |
So, | . |
try it
[ohm_question]146257[/ohm_question]Repeating Decimals
So far, in all the examples converting fractions to decimals the division resulted in a remainder of zero. This is not always the case. Let’s see what happens when we convert the fraction to a decimal. First, notice that is an improper fraction. Its value is greater than . The equivalent decimal will also be greater than .We divide by .

Repeating Decimal
A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.is the repeating digit | |
is the repeating digit | |
is the repeating block | |
is the repeating block |
example
Write as a decimal.Answer:
Solution
Divide by
Notice that the differences of and repeat, so there is a repeat in the digits of the quotient; will repeat endlessly. The first decimal place in the quotient, , is not part of the pattern. So,
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[ohm_question]146259[/ohm_question]example
Simplify:Answer: Solution
Change to a decimal. | ![]() |
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Add. |