What is 1/3 as a Decimal?

The correct answer is: $0.\overline{3}$

Explanation

Divide 1 by 3 — 3 goes into 1 zero times with remainder 1, so you write a decimal point and bring down a zero. That gives 10 divided by 3 = 3 remainder 1; the remainder repeats, so the digit 3 repeats forever. Thus $1/3$ as a decimal is $0.333\ldots$, which we write compactly as $0.\overline{3}$.

Steps:

1. $1 \div 3 = 0$ remainder $1$
2. Bring down $0$: $10 \div 3 = 3$ remainder $1$
3. Remainder repeats ⇒ digits repeat: $0.333\ldots = 0.\overline{3}$

(Algebraic check: let $x=0.\overline{3}$. Then $10x=3.\overline{3}$. Subtract: $9x=3$, so $x=\tfrac{1}{3}$.)

Note: Rounded forms are $0.33$ (2 decimal places) or $0.333$ (3 decimal places), but the exact decimal is $0.\overline{3}$.