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Expert-verified Found in: Page 616 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # 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.$3.454545...$

The given repeating decimal as a geometric series is $\sum _{k=0}^{\infty }0.45{\left(0.01\right)}^{k},$ and as the quotient of two integers reduced to lowest terms is $\frac{342}{99}.$

See the step by step solution

## Step 1. Given Information.

The given repeating decimal is $3.454545...$

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

The repeating decimal as a geometric series can be expressed as

## 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 ### Want to see more solutions like these? 