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#