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Chapter 12: Q. 180 (page 1199)

Write each repeating decimal as a fraction.

0.2

Short Answer

Expert verified

The repeating decimal as fraction is29.

Step by step solution

01

Step 1. Given information.

The repeating decimal is 0.2showing the repeating as 0.2=0.2222222.....

Now use place value to write this as sum.

0.2+0.02+0.002+0.0002+0.00002+......

The sumSof the infinite geometrical series having first term a1 and the common ratiorisS=a11-r,r<1

02

Step 2. To find a1 and r.

The first term a1=0.2and the common ratio is

r=0.020.2r=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=0.21-0.1S=0.20.9S=29

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Most popular questions from this chapter

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