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Chapter 12: Q. 182 (page 1199)

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

0.27

Short Answer

Expert verified

The repeating decimal as a fraction is311.

Step by step solution

01

Step 1. Write the given information.

The given repeating decimal is 0.27=0.27272727.....

02

Step 2. Write the repeating decimal as sum using place value.

This decimal can be written as sum of infinite series as:0.27=0.27272727....=0.27+0.0027+0.000027+....

03

Step 3. Use the formula for sum of infinite geometric series. 

The sum S for infinite series with first term, a and ratio, r is:

S=a1-r,r<1

04

Step 4. Find the first term, a and common ratio, r for the formula in Step 3. 

The first term, a=0.27and the common ratio is:

r=0.00270.27鈬�r=0.01

05

Step 5. Use the sum, S formula with a=0.27 and r=0.01 .

So,

S=a1-r鈬�S=0.271-0.01鈬�S=0.270.99鈬�S=311

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