Question

Question #7ef34

Answer 1

`97/495`

Explanation:

We require to obtain 2 equations with the same repeating part after the decimal point and subtract them to eliminate the repeating part.

`0.1bar(95)"represents " 0.1959595....`

To obtain 2 equations with the same repeating part, requires the original number to be multiplied by 10 and 1000

`"let "x=0.19595...larr" original number"`

`rArr 10x=1.bar(95)rarr(1)`

`rArr1000x=195.bar(95)rarr(2)`

We now have the repeating decimal after the decimal point in both equations and can subtract them.

`(2)-(1)`

`1000x-10x=195.bar(95)-1.bar(95)`

`rArr990x=194larrcolor(red)" no repeating decimal"`

`rArrx=194/990=97/495" in simplest form"`