What is 1/3 as a decimal?

 Set up the division

To convert 1/3 into a decimal, we divide 1 by 3. In long division, this looks like dividing 1 by 3:

1 ÷ 3

 Perform the division

1. Start with 1. Since 1 is smaller than 3, we know that the integer part of the result is 0.
2. Add a decimal point and bring down a 0, making it 10.
3. Divide 10 by 3, which gives 3. The remainder is 1 (since 3 × 3 = 9, and 10 – 9 = 1).
4. Now, bring down another 0, making it 10 again.
5. Repeat the division: divide 10 by 3, which gives another 3, with the remainder 1.
6. This process repeats indefinitely.

Recognize the repeating decimal

You’ll notice that the remainder continues to be 1, and each time we bring down a 0, the division gives a 3. This creates a repeating decimal:

     1÷3=0.3333333…(where the 3 repeats indefinitely)

Thus, 1/3 as a decimal is:

$\text{(the line over the 3 indicates it repeats infinitely)}$

Alternatively, it’s often written as approximately 0.3333 (with a few decimal places), but mathematically, it repeats forever.

Conclusion:

The decimal representation of 1/3 is 0.3333…, where the 3 repeats infinitely.