How do you convert 0.3417 (17 repeating) to a fraction?

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Answer 1 · 2016-02-24T13:14:53

$3383/9900$

$0.34bar(17)=34/100+0.00bar(17)$

$10000xx0.00bar(17)=17. bar(17)$
$100xx0.00bar(17)=0.bar(17)$

subtract the two expressions, and you will obtain:

$9900xx0.00bar(17)=17$

$0.00bar(17)=17/9900$

Now we know :

$0.34bar(17)=34/100+17/9900$

multiply the first fraction by 99/99 to get the same numerator:

$3366/9900+17/9900=3383/9900$

9900 is multiple of powers of 2,3,5 and 11.

3383 is not multiple of these prime numbers, so the fraction cannot be simplified.