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Chapter 12: Q. 177 (page 1199)

Write each repeating decimal as a fraction.

0.3

Short Answer

Expert verified

The repeating decimal as fraction is 13.

Step by step solution

01

Step 1. Given information.

The repeating decimal is 0.3showing the repeating as 0.3=0.333333......

Now use place value to write this as sum.

0.3+0.03+0.003+0.0003+0.00003+....

The sumSof the infinite geometrical series having first terma1and the common ratiorisS=a11-r,r<1

02

Step 2. To find a1 and r.

The first term a1=0.3and the common ratio is

r=0.030.3r=0.1

Because 0.1鈮�1, so the infinite geometric series have sum.

03

Step 3. To find the sum.

We have.

S=a11-rS=0.31-0.1S=0.30.9S=13

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