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Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.

0.237237237...

Short Answer

Expert verified

The given repeating decimal as a geometric series isk=00.2370.001k,and as the quotient of two integers reduced to lowest terms is79333.

Step by step solution

01

Step 1. Given Information.

The given repeating decimal is0.237237237...

02

Step 2. Express the repeating decimal as a geometric series.

The repeating decimal as a geometric series can be expressed as

0.237237237...=0.2371+0.001+0.0012+0.0013+0.0014....=k=00.2370.001k

03

Step 3. Express the repeating decimal as the quotient of two integers reduced to the lowest terms.

The given repeating decimal as the quotient of two integers reduced to the lowest terms can be expressed as

0.237237237...=0.2371+0.001+0.0012+0.0013+0.0014....=k=00.2370.001kUseS=a1-r=0.2371-0.001=0.2370.999=237999=79333

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