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Write each repeating decimal as a fraction in simplest form.

0.21¯

Short Answer

Expert verified

The simplest form is=2199

Step by step solution

01

Step 1. Interpret the notation.

0.21¯means 0.212121…..

02

Step 2. Assign a variable.

Let N = 0. 212121…...

03

Step 3. Decide by what to multiply.

Since two-digits repeat so we multiply each side by 100.

100N = 100(0.212121…..)

100N = 21.212121…..

04

Step 4. Solve for N.

Subtract N from 100N, so that the repeating part eliminates.

100N=21.212121.-N=0.212121.99N=21

Then divide each side by 99 and simplify.

99N99=2199

N=2199

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