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Chapter 1: Q21. (page 10)

Write each repeating decimal as a fraction in the simplest form.

0.13炉

Short Answer

Expert verified

The simplest form is=1399.

Step by step solution

01

Step 1. Interpret the notation.

0.13炉 means 0.131313鈥�..

02

Step 2. Assign a variable.

Let N = 0.131313鈥�...

03

Step 3. Decide by what to multiply.

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

100N = 100(0.131313鈥�..)

100N = 13.131313鈥�..

04

Step 4. Solve for N.

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

100N=13.131313鈥�.-N=0.131313鈥�.99N=13

Then divide each side by 99 and simplify.

99N99=1399

N=1399

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