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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)

[tex]10x=0.45[/tex] (45 is recurring)

=> [tex]100x =4.54[/tex] (54 is recurring)

=> [tex]1000x= 45.45[/tex] (45 is recurring)

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

[tex]1000x-10x = 45.45-0.45[/tex]

[tex]990x =45[/tex]

=> [tex]x =45/990[/tex]

Dividing by 5

=>[tex]x= 9/198[/tex]

Now dividing by 9

[tex]x =1/22[/tex]

Hence, proved.

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