Question

Write the number 0.21212121 as a fraction.

Answer 1

The answer would be 7/33

Answer 2

Explanation:

If 21 is not repeating, then it's easy.

`0.\underbrace{21212121}_8=\frac{21212121}{1\underbrace{00000000}_8}`

If If 21 is repeating, then the solution is:

`x=0.21212121...\qquad\text{multiply both sides by 100}\\\\100x=21.212121...\\\\100x-x=21.212121...-0.212121...\\\\99x=21\qquad\text{divide both sides by 99}\\\\x=(21)/(99)\\\\x=(21:3)/(99:3)\\\\x=(7)/(33)`