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# Writing repeating decimals as fractions review

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

## Writing decimals as fractions

To convert a decimal to a fraction, we write the decimal number as a numerator, and we write its place value as the denominator.
Example 1: 0, point, 07
0, point, 0, start color #11accd, 7, end color #11accd is start color #11accd, 7, end color #11accd start text, start color #1fab54, h, u, n, d, r, e, d, t, h, s, end color #1fab54, end text. So, we write start color #11accd, 7, end color #11accd over start color #1fab54, 100, end color #1fab54.
0, point, 07, equals, start fraction, start color #11accd, 7, end color #11accd, divided by, start color #1fab54, 100, end color #1fab54, end fraction

## But what about repeating decimals?

Let's look at an example.
Rewrite 0, point, start overline, 7, end overline as a simplified fraction.
Let x equal the decimal:
x, equals, 0, point, 7777, point, point, point
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:
9, x, equals, 7
Solve for x:
x, equals, start fraction, 7, divided by, 9, end fraction
Remember from the first step that x is equal to our repeating decimal, so:
0, point, start overline, 7, end overline, equals, start fraction, 7, divided by, 9, end fraction