Question

Express 16.523 in p/q form where 23 has bar

Answer 1

1) Given number, 1.32323..

Let the number be x

x = 1.3232323...

As the periodicity ( number of repeating digits after the decimal point ) of the number is 2, let's multiply the number with 10².

100x = 132.3232..

Now let's subtract x from 100x

                                     100x = 132.323232..

                              -            x =     1.323232..

                          ------------------------------------------

                                       99x = 131

                                           x = 131/99

∴1.3232323.. = 131/99

2) Given number, 3.575757..

Let the number be x

x = 3.575757...

As the periodicity ( number of repeating digits after the decimal point ) of the number is 2, let's multiply the number with 10².

100x = 357.575757..

Now let's subtract x from 100x

                                     100x = 357.575757..

                              -            x =     3.575757..

                          ------------------------------------------

                                       99x = 354

                                           x = 354/99

                                           x = 118/33

∴3.575757.. = 118/33

Hope my answer helps you : )

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Answer 2

let x=16.523232323....
1000x =16523.2323....
1000x -x=16523.2323... -16.2323
999x= 16507
x=16507/999