Question

I have already asked this doubt and i hv got the answer but i did not understand. So could u please explain it thoroughly as i lost my mark in this question.

Find the smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates after one place of decimal.

Answer 1

If we divide any number by 10 or 20 or 50 or 100 we get decimal in the remainder and for getting remainder up to one decimal digit we have to divide by 10. In general this concept u can apply as we know if denominator of any fraction is in form of 2m × 5n , So we get terminating decimal digits .

And number of decimal digits depends on " m " and " n " ( As m > n we get decimal digits = m and if n > m we get decimal digits = n ) .

So if we get denominator 2 , 5 or 10 we get decimal digits expansion terminate after one place .

We know highest the denominator smallest the number , so if we get denominator = 10 we get smallest rational number who satisfy all given condition .

And to remove 3 from denominator of given number 1/3 we have to multiply by 3 in given number , So

Our smallest rational number = 3/10