Question

X = 0.045
Prove algebraically that x can be written as 1/22

Answer 1

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.

Answer 2

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.