What is 1/3 as a Decimal?

Q: What is 1/3 as a Decimal?

The correct answer is: 0.overline3 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 0.333ldots, which we write compactly as 0.overline3. Steps: 1 ÷ 3 = 0 remainder 1 Bring down 0: 10 ÷ 3 = 3 remainder 1 Remainder repeats ⇒ digits repeat: 0.333ldots = 0.overline3 (Algebraic check: let x=0.overline3. Then 10x=3.overline3. Subtract: 9x=3, so x=(1)/(3).) Note: Rounded forms are 0.33 (2 decimal places) or 0.333 (3 decimal places), but the exact decimal is 0.overline3.

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:

$1 \div 3 = 0$ remainder $1$
Bring down $0$: $10 \div 3 = 3$ remainder $1$
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 $0.\overline{3}$.

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