Question

express 1.323 where bar is on 23 in p/q form

Answer 1

let x = 1.323 bar 

Multiply by 10,

10x = 13.23bar 

As there are 2 numbers under bar, multiply by 100,

1000x = 1323.23bar 

subtract 10x from both sides,

1000x = 1323.23 bar 
    -10x =  -13.32 bar
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990x  = 1310 [bar cancel]
_____________________

x =1310/990 

x =131/99 

then, 1.323  bar in p/q form is 131/99


i hope this will help you


(-:

Answer 2

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 : )