Question

see attachedconvert the repeating decimal to a/b form where a,b are integers and b is not equal to 0.

Answer 1

We are asked to convert the repeating decimal to fraction

`\text{Take d = 4.}\bar{\text{72}}\text{ = 4.72727272}\ldots`
`\text{ d = 4.72727272}\ldots\text{ (first equation)}`

Step 1: Multiply both sides by 100 because there are two repeating digits

`\text{ 100d = 472.727272}\ldots(\text{second equation)}`

Step 2: Subtract the first equation from the second one

`\begin{gathered} \text{ 100d -d = 472.727272 - 4,72727272} \\ \text{ 99d = 467. 99999}\ldots\text{ }\approx\text{ 4}68 \\ \text{ 99d = 4}68 \\ \text{ d =}(468)/(99)=(52)/(11) \end{gathered}`

Therefore, the fractional form of the repeating decimal 4.7277272... is 52/11