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Chapter 12: Q. 298 (page 1219)

In the following exercises, write each repeating decimal as a fraction.

0.8炉

Short Answer

Expert verified

The repeating decimal as a fraction is89

Step by step solution

01

Step 1. Given information

The given repeating decimal is0.8炉

02

Step 2. Use place value to write this as a sum.

0.8炉=0.88888888...=0.8+0.08+0.008+0.0008+0.00008+...

This is the sum of infinite series of G.P.

03

Step 3. Write the repeating decimal as a fraction.

We will find the sum of infinite G.P. to write the repeating decimal as a fraction.

a=0.8r=0.080.8r=0.1

So the sum is

S=a1-rS=0.81-0.1S=0.80.9S=89

Therefore, the repeating decimal as a fraction is 89.

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