What happens when you divide 5 into 3? The answer does not stop at one or two decimal places—the same digit keeps coming back.
The 6 repeats forever, so the exact decimal can also be written as 1.6̅.
How do you convert 5/3 to a decimal?
A fraction means division, so convert 5/3 by dividing the numerator by the denominator:
Now use long division:
- 3 goes into 5 one time, leaving a remainder of 2.
- Add a decimal point and bring down a zero, giving 20.
- 3 goes into 20 six times because 3 × 6 = 18. The remainder is 2.
- Bring down another zero, giving 20 again.
- Once again, 3 goes into 20 six times, leaving a remainder of 2.
That is why 5/3 as a decimal is a repeating decimal.
Why does 5/3 have a repeating decimal?
The key is the remainder.
After each 6, the remainder is still 2. Bringing down another zero turns that 2 into 20, so the same division happens again:
Because the remainder never becomes 0, the decimal never ends.
Is 5/3 equal to 1.67?
Yes, but there is an important difference.
Here are some common rounded forms:
| Form | Value |
|---|---|
| Exact decimal | 1.666… |
| Nearest tenth | 1.7 |
| Nearest hundredth | 1.67 |
| Nearest thousandth | 1.667 |
5/3 in different forms
The same number can be written in several ways:
What about 5 3/4 and 5 3/8 as decimals?
These are mixed numbers, so they are different from 5/3.
Quick check
If you remember just one rule, remember this:
For this problem:
The repeating 6 is not an error—it continues forever.
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