10/12 as a Decimal
10/12 = 0.8333333333333334 (repeating). The digits never stop, so the exact value is normally written with a repeating bar over the 1-digit block, and any written decimal is an approximation of it. As a percentage that is 83.33%.
Long division, step by step
Divide the numerator by the denominator the way it is done on paper: bring down a zero, note how many times the denominator fits, keep the remainder, repeat. The remainders are what decide whether the decimal stops.
| Step | Working | Digit | Remainder |
|---|---|---|---|
| 1 | 10 × 10 = 100 | 8 | 4 |
| 2 | 4 × 10 = 40 | 3 | 4 |
The remainder repeats, so the digits must repeat with it — that is the whole mechanism behind a recurring decimal, not a quirk of the calculator.
Rounded to different precisions
How many places you keep depends on the use: money stops at two, engineering often wants three or four, and a science problem usually wants significant figures rather than decimal places.
| Precision | Value | Result |
|---|---|---|
| 1 decimal place | 0.8 | rounded |
| 2 decimal places | 0.83 | rounded |
| 3 decimal places | 0.833 | rounded |
| 4 decimal places | 0.8333 | rounded |
| Percentage | 83.33% | rounded |
Will it terminate?
A fraction has a terminating decimal exactly when its simplified denominator is built only from 2s and 5s. Here the denominator reduces to 6, which carries a prime factor other than 2 or 5, so the decimal recurs with a period of 1. This is a property of the denominator alone: the numerator never decides it.
Because 10/12 reduces to 5/6, the recurrence pattern is the same as for 5/6. Simplifying first is the quickest way to see the true period.
Questions about 10/12
What is 10/12 as a decimal?
It does not terminate. The decimal begins 0.8333333333 with a repeating block of 1 digit, because the reduced denominator 6 contains a prime factor other than 2 or 5.
Is 10/12 already in simplest form?
No. Dividing both parts by their greatest common factor gives 5/6, which has the same value and a shorter representation.
How do I round 10/12 to two decimal places?
Two places give 0.83. The third digit decides it — when it is 5 or more the second digit rounds up, otherwise it stays.
What is 10/12 as a percentage?
83.33%, obtained by multiplying the decimal by 100. It is the same number with the decimal point moved two places to the right, and the same rounding rules apply.