Question

express the following in the form of p/q where p and q are integer q#0​

Answer 1

Answer:

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Step-by-step explanation:

(i) 0.6¯0.6¯ Let x = 0.6¯0.6¯ (Pure recurring decimal)

i.e. x = 0.6666 …(1)

Multiplying (1) by 10, because ones digit i.e. 6 is repeating, we get 10x = 6.6666 …(2)

Subtracting (1) from (2),

we get 10x – x = (6.6666…) – (0.6666…) ⇒ 9x = 6 ⇒ x = 6969 ⇒ x = 2323

(ii) Let x = 0.47¯0.47¯ (Mixed recurring decimal) i.e. x = 0.47777 …(1)

Multiplying (1) by 10, to make it pure recurring decimal,

we get 10x = 4.7777 …(2) Further multiplying (2) by 10, we get 100x = 47.777 ….(3)

Subtracting (2) from (3), we get 100x – 10x = (47.777…) – (4.7777…) ⇒ 90x = 43 ⇒ x = 43904390

(iii) Let x = 0.001¯0.001¯ i.e. x = 0.001001001 …(1)

Multiplying (1) by 1000, we get 1000x = 1.001001 …(2)

Subtracting (1) from (2),

we get 1000x – x = (1.001001…) – (0.001001…) ⇒ 999x = 1 ⇒ x = 1999Read more on /....