Decimal to fraction ?
2 Answers
Explanation:
In general, when you have a number of the form
where
The reason this works is because if you multiply that repeating decimal by
Therefore,
It's also simple to find
Explanation:
0. color(red)(3267)32673267....=0. bar(3267)
"the bar represents the digits being repeated"
"these form the terms of a "color(blue)"geometric sequence"
3267/10000,3267/100000000,...
"with "a=3267/10000
"and "r=a_2/a_1
rArrr=cancel(3267)/(10000cancel(0000))xx(1cancel(0000))/cancel(3267)=1/10000
•color(white)(x)S_oo=a/(1-r)
rArrS_oo=(3267/10000)/(1-1/10000)
=(3267/10000)/(9999/10000)
=3267/9999=33/101