Another repeating decimal

Number Theory Level 4

Given that $0.\overline{93939393939}= \dfrac{a}{b}$ , where $a$ and $b$ are coprime positive integers . What is $a+b$ ?

The answer is 64646464646.

1 solution

Geoff Pilling
Aug 17, 2016

$0.\overline{93939393939}= \frac{93939393939}{99999999999} = \frac{31313131313}{33333333333}$ $31313131313+33333333333=\boxed{64646464646}$

You know, that's mean 0.93939393... or it's infinite decimal which the answer 31/33 or 64

Daniel Sugihantoro - 4 years, 10 months ago

Actually its very close to 31/33, but not quite. The repeating decimal above is 0.93939393939939393939399393939393993939393939... which is equal to 31313131313/33333333333 (Almost 31/33 but not quite)

Thanks, Geoff

Geoff Pilling - 4 years, 10 months ago

A=0.9393.... 100A=93.9393.... Subtracting we get 99A=93 A=31/33 I dont get what is wrong in this approach!!!

A Former Brilliant Member - 4 years, 9 months ago

@A Former Brilliant Member – Ohhhh wait i got it....smart way to confuse :)

A Former Brilliant Member - 4 years, 9 months ago

@A Former Brilliant Member – Hahahaha... ;^)

Geoff Pilling - 4 years, 9 months ago

It's not almost, test it with calculator and the result will same

Daniel Sugihantoro - 4 years, 9 months ago

@Daniel Sugihantoro – $0.\overline{93939393939}=\frac{31313131313}{33333333333} \neq \frac{31}{33}$

Geoff Pilling - 4 years, 9 months ago

Another repeating decimal

The answer is 64646464646.

1 solution

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