Sunday

February 1, 2015

February 1, 2015

Posted by **Haile** on Thursday, September 29, 2011 at 10:54pm.

- Math -
**Reiny**, Thursday, September 29, 2011 at 11:53pm0.5131313131313...

= .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

**Answer this Question**

**Related Questions**

Math - Express the repeating decimal 0.513 (the 13 is repeating) as a fraction ...

math - 1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 A)15 B)15/2...

math(need 2nd opinion) - 1)Find a1 in a geometric series for which Sn=300,r=-3,...

sequence and series - express the given repeating decimal 0.159159159 as a ...

math - Find the mixed number or rational fraction in lowest terms represented by...

Math - How do you rename as a fraction and decimal 55 5/9% You should know that ...

6th grade math - Please check to make sure I did these correctly, so confusing. ...

Math 115 - Every fraction has a decimal equivalent that either terminates (for ...

Math 115 - Every fraction has a decimal equivalent that either terminates (for ...

Math - Rename each repeating decimal as a fractio in lowest terms. Use Let ...