Express the following in the form p/q, where p and q are integers and

(i) (ii)

(iii)

(i) 0.͞6 = 0.666…

Let x = 0.666666…

Multiplying both sides by 10

10x = 6.666

10x = 6 + x

9x = 6

x = 2/3

(ii) 0.47͞ = 0.4777…

= 4/10 + 0.777/10

Let x = 0.777…

Multiplying both sides by 10

10x = 7.777…

10x = 7 + x

x = 7/9

+ = +

= 43/90

(iii) 0.0͞0͞1 = 0.001001…

Let x = 0.001001…

Multiplying both sides by 1000

1000x = 1.001001…

1000x = 1 + x

999x = 1

x = 1/999

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