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Chapter 1: Q22. (page 10)

Write each repeating decimal as a fraction in simplest form.

0.21炉

Short Answer

Expert verified

The simplest form is=2199

Step by step solution

01

Step 1. Interpret the notation.

0.21炉means 0.212121鈥�..

02

Step 2. Assign a variable.

Let N = 0. 212121鈥�...

03

Step 3. Decide by what to multiply.

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

100N = 100(0.212121鈥�..)

100N = 21.212121鈥�..

04

Step 4. Solve for N.

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

100N=21.212121鈥�.-N=0.212121鈥�.99N=21

Then divide each side by 99 and simplify.

99N99=2199

N=2199

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