Posted by **lili** on Monday, April 12, 2010 at 2:10am.

express the given repeating decimal

0.159159159 as a fraction

- sequence and series -
**Damon**, Monday, April 12, 2010 at 5:00am
n = 0.159159159...

three numbers 159 repeat

so multiply by 10^3 = 1000

1000n =159.159159159 now subtract n

n = .159159159

-------------------------------

999n = 159.000000....

so

n = 159/999

- sequence and series -
**Damon**, Monday, April 12, 2010 at 5:29am
or

159*10^-3 + 159*10^-6 +159*10^-9 ....

each term is 10^-3 times previous

sum of infinite geometric series with first term g and ratio r

S = g/(1-r)

here g = .159

and r = .001

so

S = .159/(1-.001) = .159/.999 =159/999

## Answer This Question

## Related Questions

- Math - Express the repeating decimal 0.513 (the 13 is repeating so the decimal ...
- Math - Express the repeating decimal 0.513 (the 13 is repeating) as a fraction ...
- math - Tell me whether each fraction. 1/n, is given as a terminating decimal or ...
- math - You are given a fraction in simplest form. The numerator is not zero. ...
- Algebra 1 - Express each fraction as a terminating or repeating decimal. 2/25, 5...
- Urgent math - Express the repeating decimal as a fraction. 0.156156156...
- 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,...
- math - Express the repeating decimal 0.2323 as a geometric series, and write its...
- Math - How do you rename as a fraction and decimal 55 5/9% You should know that ...

More Related Questions