Question

Write the recurring decimal 0.45....... as a fraction.

Answer 1

Given the following question:

We are given the repeating decimal of 0.45

We will use the formula:

`\begin{gathered} ((d*10^r)-n)/(10^r-1) \\ (0.45*10^2)-0)/(10^2-1) \\ \text{ Simplify} \\ (0.45*2\cdot10^2)/(10^2-1)=(45)/(99) \\ \text{ Simplify once more} \\ (45)/(99)/9=(5)/(11) \\ =(5)/(11) \end{gathered}`