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

Question

2069 views around the world

You can reuse this answer
Creative Commons License

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.