How do I convert a fraction with an awkward denominator into a decimal?
Quick answer
Divide the numerator by the denominator. For example, 5 ÷ 6 gives 0.8333…; the 3 repeats, so the exact decimal is 0.8\overline{3}. If an exact repeating decimal is not needed, report a rounded approximation at the precision the task calls for: to the nearest hundredth, 5/6 is 0.83; to the nearest thousandth, it is 0.833. State the precision when you give an approximation.
The question, the details, the next step.
I have a fraction like 5/6, and the denominator does not turn neatly into tenths or hundredths. What should I do?
Use division: divide the numerator by the denominator. For 5/6, calculate 5 ÷ 6. Since 6 does not go into 5 as a whole number, write 0 and a decimal point, then continue the division by adding zeros after the 5.
Here is the calculation:
- 6 goes into 50 eight times, with remainder 2. That gives 0.8 so far.
- Bring down a zero to make 20. Six goes into 20 three times, with remainder 2.
- The remainder is still 2, so bringing down another zero gives 20 again. The 3 continues to repeat.
So 5/6 = 0.8333… exactly, or 0.8\overline{3} using a bar to show the repeating digit. Division can produce a repeating decimal when a remainder recurs. [S1]
How do I know whether to keep writing digits or round the answer?
First check what the problem asks for. If it asks for an exact answer, keep the fraction or write the repeating decimal with a bar: 5/6 = 0.8\overline{3}. If it asks for a decimal approximation, use the requested precision. If none is given, choose a precision that suits the purpose and say what you chose.
For example, to the nearest hundredth, 5/6 is approximately 0.83. To the nearest thousandth, it is approximately 0.833. These are approximations, not replacements for the exact value. There is no single rounding precision that fits every task; the needed precision depends on the problem. [S1]
Can you show how those rounded forms relate to the repeating decimal?
Start with the exact decimal, 0.8333… . To the nearest hundredth, the reported approximation is 0.83; to the nearest thousandth, it is 0.833. The number of decimal places you report depends on the precision the task calls for.
Label the result so its precision is clear—for example, write “5/6 ≈ 0.83, to the nearest hundredth.” That makes clear you are giving an approximation rather than the exact value. The exact value remains 5/6, or 0.8\overline{3}.
What is a quick way to present the answer so I do not confuse an exact value with an approximation?
Put the exact value and the rounded form on separate, clearly labeled parts of your answer. For this example, you could write:
“5/6 = 0.8\overline{3} exactly. To the nearest hundredth, 5/6 ≈ 0.83.”
The equals sign states an exact equality; the approximation sign indicates that 0.83 is rounded. If your class or task uses a different notation, follow that convention, but keep the distinction clear. The division method gives the decimal digits; the task’s instructions guide how many rounded digits to report.
A practical checklist
Divide the numerator by the denominator.
Continue the division with decimal places if there is a remainder.
If a remainder recurs, check whether the decimal digits repeat.
Keep the fraction or use repeating-decimal notation when an exact answer is needed.
For an approximation, follow the requested precision and state how you rounded.
Use an approximation sign for a rounded decimal rather than presenting it as exact.
A few more useful answers
What if I am not told how many decimal places to use?
Check the context or any instructions for the expected precision. If there is no guidance, choose a useful number of places and label it, such as “to the nearest hundredth.”
Can I leave the answer as a fraction instead?
Yes, if the task allows an exact fraction. A fraction such as 5/6 is exact, while a rounded decimal such as 0.83 is an approximation.
How do I show that a digit repeats?
Use a bar over the repeating digit or group of digits: 0.8\overline{3} means 0.8333… . You can also use an ellipsis when the repeating pattern is clear.
Sources
References used for this guide.
- [S1] Decimals and Fractions — OpenStax Prealgebra 2e openstax.org · Checked