# Math

Express the repeating decimal 0.513 (the 13 is repeating so the decimal is 0.5131313131313...) as a fraction in lowest terms using the infinite geometric series method.

1. 👍 0
2. 👎 0
3. 👁 226
1. 0.5131313131313...
= .5 + .013131313...
= .5 + .013 + .00013 + .0000013 + ...
= .5 + an infinite geometric series

for the GS, a= .013 , r = .01
sum ∞ = a/(1-r) = .013/(1-.01) = (13/1000) / (99/100)
= 13/990

so sum∞ = 1/2 + 13/990 = 254/495

easier way:
for numerator, write down all digits to the end of the first repeat, from that subtract the digits that don't repeat : 513 - 5 = 508

for denominator, write down a 9 for each repeating digit, followed by a 0 for each non-repeating digit : 990
so ..

.5131313 = 508/990 = 254/495

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### Math

Express the repeating decimal 0.513 (the 13 is repeating) as a fraction in lowest terms using the infinite geometric series method.

asked by Haile on September 29, 2011
2. ### Math

What is 5/9 written as a decimal? 0.45 0.4 repeating 0.5 0.5 repeating What is 0.26 written as a fraction in simplest form? 26 over 100 13 over 50 26 over 10 13 over 25 In a fraction with a denominator of 15,which value could the

asked by Help ms.sue on October 2, 2017
3. ### Math

Which one of the following is an example of a repeating decimal? A. 0.6666666(W/ repeating sign) B. 1.234545 C. 0.123321 D. 6.787878(W/ repeating sign) I think its A but D is also repeating. If I'm wrong please elaborate

asked by Jocelynn on December 19, 2015
4. ### Algebra 1

Order the given numbers from least to greatest. 1. -√9, 2π, -1, 5.12(repeating decimal), -7/2 A: -7/2, -√9, -1, 5.12 (repeating decimal), 2π? Also, is -√9 a real and rational number?

asked by Victoria on September 2, 2014
5. ### College Math

Express each decimal of integers, in simplest form. 0.1 with the repeating decimal 1

asked by Pumpkin on December 11, 2007

Please check to make sure I did these correctly, so confusing. Thank you. Rename each fraction as a terminating or repeating decimal 13/20 .65 1/3 0.3333333333333333 2/9 0.2222222222222222 5/12 0.4166666666666667 1/16 0.0625

asked by claire on May 13, 2012
7. ### math

Tell me whether each fraction. 1/n, is given as a terminating decimal or a repeating decimal for the given rules of n. Write t for terminating or r for repeating. It starts at 2- 10 which are t and r.

asked by Wossum on September 3, 2016
8. ### Math-Decimals

Please match each number with its best example. Some values will need to be changed into a decimal format. A. Recurring Decimal B. Mixed Number C. Non-repeating Decimal D. Finite Decimal E. Decimal Examples: ½ 5½ π 0.375 ⅓ I

asked by Ally on January 30, 2012
9. ### Math

Please match each number with its best example. Some values will need to be changed into a decimal format. A. Recurring Decimal B. Mixed Number C. Non-repeating Decimal D. Finite Decimal E. Decimal Examples: ½ 5½ π 0.375 ⅓ I

asked by Jess on January 31, 2012
10. ### Math

Please match each number with its best example. Some values will need to be changed into a decimal format. A. Recurring Decimal B. Mixed Number C. Non-repeating Decimal D. Finite Decimal E. Decimal Examples: ½ 5½ π 0.375 ⅓ I

asked by Ally on January 30, 2012

More Similar Questions