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Chapter 12: Q. 179 (page 1199)

Write each repeating decimal as a fraction.

0.7

Short Answer

Expert verified

The repeating decimal as fraction is79.

Step by step solution

01

Step 1. Given information. 

The repeating decimal is 0.7showing the repeating as 0.7=0.7777777......

Now use place value to write this as sum.

0.7+0.07+0.007+0.0007+0.00007+....

The sumS of the infinite geometrical series having first term a1and the common ratiorisS=a11-r,r<1

02

Step 2. To find a1 and r.

The first term a1=0.7and the common ratio is

r=0.070.7r=0.1

Because0.1鈮�1, so the infinite geometric series have sum.

03

Step 3. To find the sum.

We have,

S=a11-rS=0.71-0.1S=0.70.9S=79

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