Question

What is 4.45 repeating as a fraction?

Answer 1

This would be 49/11.

Hope this helps!

Answer 2

$\bf x=4.454545\overline{45}$

now, let's multiply "x" by a power of 10, so that, the repeating part, ends up at the left-hand-side of the decimal point, so, in this case, we need to move 45 over to the left, so, we'll multiply "x" by 100.

$\bf \begin{array}{llcll} 100\cdot x&=&445.454545\overline{45}\\ &&\uparrow \\ &&441+4.454545\overline{45}\\ &&\uparrow\\ &&441+x \end{array} \\\\\\ 100x=441+x\implies 99x=441 \implies x=\cfrac{441}{99}\implies x=\cfrac{49}{11}$