Question

Express (i) 0.00323232.....and (ii) 2.0151515....... in the form of p/q, where p and q are integers and q not equal to 0. Can anybody do it ?

Answer 1

In such problems the key is to eliminate the recurring values after the decimal. This can be achieved using the following method :-



1)  Let x = 0.00323232.......(i)


Multiply equation (i) by 100 on both sides,

100 x = 0.323232.......(ii)


Multiply equation (i) by 10,000 on both sides,

10,000 x = 32.323232.......(iii)

Subtracting equation (ii) from (iii),

          10,000 x = 32.323232.......(iii)
        --     100 x = 0.323232.......(ii)
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             9900 x = 32

Thus, x = 32 / 9900

2) Let x = 2.0151515.......(i)


Multiply equation (i) by 1000 on both sides,

1000 x = 2015.1515.......(ii)


Multiply equation (i) by 10 on both sides,

10 x = 20.151515.......(iii)

Subtracting equation (iii) from (ii),

          1000 x = 2015.1515.......(iii)
        --   10 x = 20.151515.......(ii)
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             990 x = 1995

Thus, x = 1995 / 990

Therefore the p/q forms are  32 / 9900  and 1995 / 990

Answer 2

Answer:

the p/q forms are 32/9900 and 1995/990