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For how many integer values of  between 1 and 474 inclusive does the decimal representation of \(n/30\) terminate?

 Jan 11, 2022
 #1
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https://web2.0calc.com/questions/help-with-decimals

 

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 Jan 11, 2022
edited by AlgebraGuru  Jan 11, 2022
 #2
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The link provided below has a correct answer, but the answerer didn't explain why it only works if it is divisible by 3.

First off, if you have a fraction n/2, then you can have any n in order to repeat

If you have a fraction n/3, then we need a multiple of 3

if we have a fraction n/5, then you can have any n

so we need a multiple of 3 in order to repeat

thus, the answer is 474/3 (if its divisible) or ceil(474/3) (if it's not divisible.)

it's divisible, so the answer is 474/3=158

 Jan 11, 2022

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