Question

Express 0.237- in which on top of 37 there is bar- as the quotient of two integers having no common factors

Answer 1

Answer:

0.23737...= 47/198

Step-by-step explanation:

Expressing decimals as fractions

Since we are given that

                x = 0.2373737......                     ----------(1)    

Multiplying by 10 on both sides we get

            10x = 2.373737.....                  -------------(2)

Multiplying by 100 on both sides we get

       1000x = 237.3737......               --------(3)  

Subtracting equation (2) from (3) we get

1000x - 10x = 237.3737... - 2.3737.....

         990x = 235    

                x = 235/990

Dividing and Multiplying by 5 we get

                x = 47/198

Hence

0.23737...= 47/198

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