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Express the number 0.3178 in the form of rational number a/b .

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Solution:

=> x = 0.3178178178… ….(i)
Multiplying both sides of (i) by 10, we get
10x = 3.178178… ….(ii)
Multiplying both sides of (i) by 10000, we get
10000x = 3178.178… ….(iii)
Subtracting (ii) from (iii), we get
9990x = 3175​

=> x = 3175/9990 = 635/1998

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