# Writing repeating decimals as fractions review

Review converting repeating decimals to fractions, and then try some practice problems.

## Skriv decimaltal som brøker

To convert a decimal to a fraction, we write the decimal number as a numerator, and we write its place value as the denominator.
Eksempel 1: $0{,}07$
$0{,}0\blueD7$ er $\blueD7$ $\text{\greenD{hundrededele}}$, så vi skriver $\blueD7$ over $\greenD{100}$.
$0{,}07=\dfrac{\blueD7}{\greenD{100}}$

## But what about repeating decimals?

Let's look at an example.
Rewrite $0.\overline{7}$ as a simplified fraction.
Let $x$ equal the decimal:
$\large{x = 0.7777...}$
Set up a second equation such that the digits after the decimal point are identical:
\large{\begin{aligned} 10x &= 7.7777...\\ x &= 0.7777... \end{aligned}}
Subtract the two equations:
$\large{9x = 7}$
Solve for $x$:
$\large{ x = \dfrac{7}{9}}$
Remember from the first step that $x$ is equal to our repeating decimal, so:
$\large{0.\overline{7}=\dfrac79}$