Question

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

A

(ii) only

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B

(i) and (iii)

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C

(i) 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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