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McGraw Hill Glencoe Algebra 2, 2012

MH

McGraw Hill Glencoe Algebra 2, 2012 View details

4. Infinite Geometric Series

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Exercise 35 Page 687

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

$\frac{5 3}{1 6 5}$

Practice makes perfect

We want to write the repeating decimal $0.3 \overline{21}$ 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	$0.3 \overline{21}$
Sum of Decimals	$0.3 + 0.021 + 0.00021 + 0.0000021 + \dots$
Sum of Fractions	$\frac{3}{1 0} + \frac{2 1}{1 0 0 0} + \frac{2 1}{1 0 0 0 0 0} + \frac{2 1}{1 0 0 0 0 0 0 0} + \dots$

Consider the sum of fractions above. Note that from the

2^{nd}

term on, we can think of it as a geometric series that has a first term of

a_{1} = \frac{2 1}{1 0 0 0} .

Let's find its common ratio

r .

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Subchapter links

Check Your Understanding p.686

H.O.T. Problems p.688

Standardized Test Practice p.689

Spiral Review p.689

Skills Review p.689