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Chapter 1: Q20. (page 10)

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

0.4炉

Short Answer

Expert verified

The simplest form is =49.

Step by step solution

01

Step 1. Interpret the notation.

0.4炉means 0.4444鈥�..

02

Step 2. Assign a variable.

Let N = 0.4444鈥�...

03

Step 3. Decide by what to multiply.

Since only one-digit repeats so we multiply each side by 10.

10N = 10(0.4444鈥�..)

10N = 4.4444鈥�..

04

Step 4. Solve for N.

Subtract N from 10N, so that the repeating part eliminates.

10N=4.4444鈥�.-N=0.4444鈥�.9N=4

Then divide each side by 9 and simplify.

9N9=49

N=49

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