Repeating decimal question...?

Question

The repeating decimal 0.34171717...can be represented by the fraction a/b where 'a' and 'b' are positive integers with no common factors greater than one. Find the sum of 'a' and 'b' and please show your work

Answer 1

0.34171717 = x

34.171717 = 100x

so 34.171717 = 100x

-0.34171717 = x

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     33.83=99x

33 83/100=99x

3383/100=99x

3383/100*99=x

3383/9900=x

i think this is right

a+b=13283

Answer 2

0.34171717...=

0.34+0.0017+0.000017+0.00000017+....=

34/100+(17/10^4)(1+1/10^2+1/10^4+...)=

34/100+(17/10^4)(100/99)=-----(100/99 is the sum of the G.P.)

3383/9900

So, a=3383,b=9900 &

a+b=13283