Question

3. The following real numbers have decimal expansions as given below. In each cas
decide whether they are rational or not. If they are rational, and of the form , what can you say about the prime factors of q?
(i) 43.123456789
(ii) 0.120120012000120000... (iii) 43.123456789
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Answer 1

Answer:

3.(i) 43.123456789

43123456789/ 1000000000 => 43123456789/10^9 => 43123456789 / 2^9 x 5^9

So, the prime factors of q = 2^9 x 5^9

(ii) 0.120120012000120000...

it has not terminating repeating decimal expansion

So, it is an irrational number

(iii) 43.123456789

let x = 43.123456789 (here a bar is given after decimal point) ------ (1)

on multiplying eq. (1) by 1000000000 we get,

1000000000x = 43123456789.123456789 (bar) ----- (2)

on subtracting eq. (1) from eq.(2) we get,

1000000000x -x = 43123456789.123456789(bar) - 43.123456789(bar)

999999999x = 43123456746

x = 43123456746/ 999999999

factors of q = 999999999

Answer 2

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