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# decimal

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Convert 0.054054054... to a fraction.

Aug 26, 2020

#1
0

Take the reciprocal of it and you get 1 / 18.5

18.5 can be written as: 18 1/2 = 37 / 2

You want the reciprocal of 37 / 2, then all you do is flip it and it becomes:

2 / 37 - That is it.

Aug 26, 2020
#3
+1042
+1

Sorry, but I am a bit confused on why the reciprocal is needed....could you explain? Thanks! (I think OP meant a repeating decimal, not division?)

:)

ilorty  Aug 26, 2020
#4
0

0.054054054... to a fraction.  Iwill make it EASIER for you to understand:

1 / 0.0540540540.....  = 1 / 18.5  x  2/2 =2 /37

Guest Aug 26, 2020
#2
+1042
+1

----

I am assuming you mean 0.054   (Sorry, latex not working...)

Since this is a repeating decimal, we put it over [ the amount of spaces after the decimal * 9 ] (not multiplied, just that amount of 9's: ex if there was 7 spaces after the decimal, it would be 9999999)

This is 3 * 9 = 999

Now, we put 54 in the numerator:

54       6

----- = -----

999    111

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Therefore, the answer is  | 6/111 |  (yikes, this is much uglier than the /boxed{} command)

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:)

Aug 26, 2020