Question

Write repeating decimal as a fraction 0.2045454545

Answer 1

First, we need to move the decimal point directly in front of the repeating part. To do this, we need to move it two places to the right, which we can do by multiplying by 100.

100 × 0.2045454545 = 20.45454545

Now we need to subtract our original number.

$\ 20.454545...\\\underline{-0.204545...}\\20.25$

Now we put that over 99 (that's one less than our 100 from earlier)

$\frac{20.25}{99}$

Our fraction is shaping up, but we shouldn't have a decimal in there. Let's multiply the top and bottom by 100 to get rid of it.

$\frac{2025}{9900}$

We're going to have to do some simplifying. (the top and bottom are both clearly divisible by 5 and then some)

$\frac{2025}{9900}=\frac{405}{1980}=\frac{81}{396}=\frac{27}{132}=\boxed{\frac{9}{44}}$  done!