Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
4. Finding Sums of Infinite Geometric Series
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Exercise 6 Page 438

Write the given number as a sum of decimals. Then, write those decimals as fractions.

Practice makes perfect

We want to write the repeating decimal as a fraction. To do so, we will start by writing this number as a sum of decimals and as a sum of fractions.

Number
Sum of Decimals
Sum of Fractions
Consider the sum of fractions above. Note that we can think of it as a geometric series that has a first term of To find its common ratio we can divide any term of the sequence by its previous term. For simplicity, we will divide by
Evaluate
Each term of the sequence can be obtained by multiplying the previous term by the common ratio
Let's substitute and in the formula for the sum of an infinite geometric series.
Evaluate right-hand side
We found that the series formed by the sum of the terms is With this information, we can express the given decimal as a fraction.