x= $0. ¯ ¯¯¯¯ ¯ 18$ , then which of the following statement are true?
(i) 100 x = $18. ¯ ¯¯¯¯ ¯ 18$
(ii) 100 x- x = $17. ¯ ¯¯¯¯ ¯ 18$
(iii) 99 x = $18$

(i), (ii) and (iii) only

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(i) and (ii) only

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(i) only

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(i) and (iii) only

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Solution

The correct option is D (i) and (iii) only
Let $x = 0. ¯ ¯¯¯¯ ¯ 18$ -----(1)
Multiply both sides of equation (1 ) by 100, we get
100 x = $18. ¯ ¯¯¯¯ ¯ 18$ ------(2)

Subtracting (1) from (2), we get

99 x = 18
Therefore,only step (i) and (iii) are correct in the conversion of recuring decimals to fractions.

Suggest Corrections

Similar questions

If $x = 0. ¯ 18$ , which of the following statements are true?

(i) $100 x = 18. ¯ 18$
(ii) $100 x - x = 17. ¯ 18$
(iii) $99 x = 18$

If $x = 0. ¯ 18$ , which of the following statements are true?

(i) $100 x = 18. ¯ 18$
(ii) $100 x - x = 17. ¯ 18$
(iii) $99 x = 18$

x = 0. ¯ ¯¯¯¯ ¯ 18

100 x = 18. ¯ ¯¯¯¯ ¯ 18

100 x - x = 17. ¯ ¯¯¯¯ ¯ 18

99 x = 18

x = \frac{1}{2}, y = 1, z = 2

x^{100} {y^{99} z}^{99} + x^{99} y^{100} z^{99} + x^{99} y^{99} z^{100} = . .

If $x = 0. ¯ ¯¯¯¯ ¯ 17$ , then which of the following statements are true?

(i) $100 x = 17. ¯ ¯¯¯¯ ¯ 17$
(ii) $100 x - x = 16. ¯ ¯¯¯¯ ¯ 17$
(iii) $99 x = 17$

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