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Question

If x=0.¯¯¯¯¯¯18, which of the following statements are true?
(i) 100x=18.¯¯¯¯¯¯18
(ii) 100xx=17.¯¯¯¯¯¯18
(iii) 99x=18


A

(i) only

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B

(i) and (iii)

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C

(ii) only

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D

(i) and (ii)

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Solution

The correct option is B

(i) and (iii)


The simplest way of representing a simple fraction is by eliminating the recurring decimal. This can be done by a multiplying factor which can be 10 or 100 or any other number depending on the number of recurring digits.

x=0.¯¯¯¯¯¯18 ....(I)

100x=18.¯¯¯¯¯¯18 (multiplied by 100 because there are only two repeating digits) ….(II)

Subtracting (I) from (II),

99x=18

Hence, the correct combinations are (i) and (iii).


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