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Express the following in the form p/q , where p and q are integers and q ≠ 0 :
(i) Let x = 0.6
x = 0.6666... ...(i)
Multiplying by 10 both sides
10x = 6.6666... ...(ii)
Subtracting eq. (i) from (ii), we get
9x = 6
x = 6/9 = 2/3
Hence, 0.6 = 2/3
(ii) Let x = 0.47
x = 0.47777... ...(i)
Multiplying eq. (i) by 10
10x = 4.7777... ...(ii)
Multiplying eq. (i) by 100
100x = 47.7777... ...(iii)
Subtracting eq. (ii) from (iii), we get
90x = 43
x = 43/90
Hence, 0.47 = 43/90
(iii) Let x = 0.001
x = 0.001001001... ...(i)
Multiplying eq. (i) by 1000, we get
1000x = 1.001001001... ...(ii)
Subtracting eq. (i) from (ii), we get
999x = 1
x = 1/999
Hence, 0.001 = 1/999
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