# How do you write the fraction 2/3 as a decimal?

Mar 19, 2018

$0. \overline{6}$

#### Explanation:

If we put in a calculator $\frac{2}{3}$ and convert it into fraction, it would display $0.6666 \ldots$ with infinite sixes.

We could also write it as $0. \overline{6}$.

Mar 19, 2018

$= 0.67$

#### Explanation:

To convert a fraction into decimal, just take the number on top which we called the numerator and divide it by the number at the bottom which we called the denominator.

$\frac{2}{3} = 0.67$

May 18, 2018

$2 \div 3 = 0.6666666 \ldots$ which can be given as $0. \dot{6} \mathmr{and} 0. \overline{6}$

Rounding gives $0.67 \mathmr{and} 0.667$ etc

#### Explanation:

To change a fraction into a decimal, you treat it as a division.

$\frac{3}{4}$ means $3 \div 4$

$\text{ } 4 | \underline{{3.0}^{2} 0}$
$\textcolor{w h i t e}{\times \times} 0.75$

The working is:

$3 \div 4 = 0$ bring down the decimal point,
$30 \div 4 = 7$ carry the remainder of 2 to make $20$
$20 \div 4 = 5$

However, sometimes you get a recurring decimal.
$\frac{2}{3} = 2 \div 3$ is such a case.

$\text{ } 3 | \underline{{2.0}^{2} {0}^{2} {0}^{2} {0}^{2} 0}$
$\textcolor{w h i t e}{\times \times} 0.6 \textcolor{w h i t e}{.} 6 \textcolor{w h i t e}{.} 6 \textcolor{w h i t e}{.} 6 \textcolor{w h i t e}{.} 6 \ldots .$

The working is:

$2 \div 3 = 0$ bring down the decimal point.
$20 \div 3 = 6$ and carry the remainder $2$ to make $20$
$20 \div 3 = 6$ and carry the remainder $2$ to make $20$
$20 \div 3 = 6$ and carry the remainder $2$ to make $20$
$20 \div 3 = 6$ and carry the remainder $2$ to make $20$
etc...

This gives the recurring decimal $0.6666666 \ldots .$
It can be written as $0. \dot{6} \text{ } \mathmr{and} 0. \overline{6}$ but is often rounded to one, two or three decimal places, depending on the level of accuracy required.

2/3 ~~ 0.7 ~~0.67 ~0.667