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does 1/40 repeat?

 Oct 25, 2017
 #1
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No......any fraction that can be written with a denominator of 2  or  5 -   or both - raised to some  positive integer power  will always terminate

 

To see this....note that 1/2  = .5

 

But  a terminating decimal raised to any positive power will itself terminate

 

Likewise...... 1/5  = .2     and for the same reason, this raised to any positive integer power will also terminate

 

So.....their products will also terminate

 

1/40  =   (1/2)^3 * ( 1/5)^1  =   .5^3 * .2  =  .025

 

 

cool cool cool

 Oct 25, 2017

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