Question

Express the following in the form , where p and q are integers and q +0.
() 0.6
(ii) 0.47
(iii) 0.001​

Answer 1

HERE IS YOUR FULL ANSWER

Answer 2

Answer:

(i) Let x = 0.6¯ = 0.6666… … (1)

As there is only one repeating digit,

multiplying (1) by 10 on both sides, we get

10x = 6.6666… … (2)

Subtracting (1) from (2), we get

10x – x = 6.6666… -0.6666…

⇒ 9x = 6 ⇒ x = 69 = 23

Thus, 0.6¯ = 23

(ii) Let x = 0.47¯ = 0.4777… … (1)

As there is only one repeating digit, multiplying (1) by lo on both sides, we get

10x = 4.777

Subtracting (1) from (2), we get

10x – x = 4.777…… – 0.4777…….

⇒ 9x = 4.3 ⇒ x = 4390

Thus, 0.47¯ = 4390

(iii) Let x = 0.001¯¯¯¯¯¯¯¯ = 0.001001… … (1)

As there are 3 repeating digits,

multiplying (1) by 1000 on both sides, we get

1000x = 1.001001 … (2)

Subtacting (1) from (2), we get

1000x – x = (1.001…) – (0.001…)

⇒ 999x = 1 ⇒ x = 1999

Thus, 0.001¯¯¯¯¯¯¯¯ = 1999

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