How to Convert Fraction to Decimal Without a Calculator
A fraction is a division. 3/4 means 3 divided by 4, and 7/8 means 7 divided by 8. If the denominator can become 10, 100, or 1000, the decimal stops. If it cannot, the decimal may repeat. Estimate first so a reversed division does not look believable.
Use a Power of 10
This is the fast method when the simplified denominator has only 2 and 5 as prime factors. 1/2 = 5/10 = 0.5. 3/4 = 75/100 = 0.75. 3/5 = 6/10 = 0.6. 7/8 = 875/1000 = 0.875. Multiply the top by the same number you used on the bottom.
Use Long Division When It Repeats
For 1/3, 3 does not go into 1, so write 0 and divide 10 by 3. The remainder is 1 again, so the 3 never stops: 0.333.... For 5/6, the result is 0.8333... because 6 includes a factor of 3. A bar over the repeating digit means it continues. The cutoff 0.33 is only an approximation of 1/3.
Check the Answer
A mixed number is a whole number plus a fraction. 2 3/5 is 2 + 0.6 = 2.6. Simplify before you divide: 6/8 is 3/4, which is 0.75. Multiply a terminating decimal back by the denominator. 0.875 × 8 = 7, so 7/8 is right. The fraction calculator can confirm the arithmetic after you have an estimate.
Frequently Asked Questions
Does every fraction have a decimal?
Yes. Divide the numerator by the denominator. Some decimals stop, and some repeat.
How can I tell that a decimal will stop?
After you simplify, the denominator's only prime factors should be 2 and 5.
What does a bar over a digit mean?
That digit repeats forever. A bar over the 3 in 0.3 means exactly 1/3.
Should I simplify first?
Yes. A smaller denominator is easier to divide and easier to check.
What if my division goes the wrong way?
The decimal will be far from your estimate. 7/8 should be near 0.9, not near 0.1.