Question

Find the prime factorisation of the denominator of rational number expressed as 6.12 bar in simplest form.

Answer 1

Let the value of x = 6.12 bar

x = 6.121212121212…

Multiply 100 on both side

100 x = 612.12121212121…..

100x = 606 + 6.12121212…

100x = 606 + x

100x – x = 606

99x = 606

X = 606/99 = 203/33

The rational number = 101 * 2 / 3 * 11

The denominator is 3 * 11 = 33

Answer 2

Step-by-step explanation:

let value of x=6.12bar

x=6.1212121212.........

multiply 100 on both sides

100x=612.121121121121.............

100x=606+6.121121121...........

100x=606+x

100x-x=606

99x=606

x=606/99=203/33

the rational no.=101×2/3×11

the denominator is 3 ×11 =33