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Verified Answer :

MissPhiladelphia

The least decimal place in 0.045 is found in the thousandths place. Thus, if expressed as a fraction, it would be 45/1000. Let's substitute this to the equation:

x = 45/1000
1000x = 45
(1000/45)x = 1
 
When you divide 1000 by 45, the quotient would be 22.2222222... This could be round to the nearest whole number which is 22. Then,

22x = 1
x = 1/22

I hope I was able to answer your question. Have a good day.

Answer:

Lets suppose this number is recurring, then we can prove.

x=0.045 (45 is recurring)

\(10x=0.45\) (45 is recurring)

=> \(100x =4.54\) (54 is recurring)

=> \(1000x= 45.45\) (45 is recurring)

We will subtract 1000x-10x to get rid of the decimals:

\(1000x-10x = 45.45-0.45\)

\(990x =45\)

=> \(x =45/990\)

Dividing by 5

=>\(x= 9/198\)

Now dividing by 9

\(x =1/22\)

Hence, proved.

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