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 blueD, 7, end color blueD is start color blueD, 7, end color blueD start color greenD, h, u, n, d, r, e, d, t, h, s, end color greenD. So, we write start color blueD, 7, end color blueD over start color greenD, 100, end color greenD.
0, point, 07, equals, start fraction, start color blueD, 7, end color blueD, divided by, start color greenD, 100, end color greenD, 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:
10x=7.7777...x=0.7777...\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
Want to learn more about writing repeating decimals as fractions? Check out this video.

Practice

Problem 1
Rewrite as a simplified fraction.
0, point, start overline, 2, end overline, equals, question mark
  • Your answer should be
  • a proper fraction, like 1, slash, 2 or 6, slash, 10
  • an improper fraction, like 10, slash, 7 or 14, slash, 8
  • a mixed number, like 1, space, 3, slash, 4

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