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: 0,070{,}07
0,070{,}0\blueD7 er 7\blueD7 hundrededele\text{\greenD{hundrededele}}, så vi skriver 7\blueD7 over 100\greenD{100}.
0,07=71000{,}07=\dfrac{\blueD7}{\greenD{100}}

But what about repeating decimals?

Let's look at an example.
Rewrite 0.70.\overline{7} as a simplified fraction.
Let xx equal the decimal:
x=0.7777...\large{x = 0.7777...}
Set up a second equation such that the digits after the decimal point are identical:
10x=7.7777...x=0.7777...\large{\begin{aligned} 10x &= 7.7777...\\ x &= 0.7777... \end{aligned}}
Subtract the two equations:
9x=7\large{9x = 7}
Solve for xx:
x=79\large{ x = \dfrac{7}{9}}
Remember from the first step that xx is equal to our repeating decimal, so:
0.7=79\large{0.\overline{7}=\dfrac79}
Want to learn more about writing repeating decimals as fractions? Check out this video.

Øvelsesopgaver

Want to try more problems like this? Check out this exercise.