Question

The following real numbers have decimal expansions as given bellow. In each case decide whether they are rational or not. If they are rational, then write in the form of where p and q are integers and having no common factors. Also express q in the
form of 2m x 5n
(1) 43.123456789 (ii) 0.120120012000 120000..... (iii) 43.123456789​

Answer 1

Answer:

(i),(iii) is rational,(ii) is irrational, (iii)

Step-by-step explanation:

(i)

As it has a terminating decimal expansion it is rational.

43.123456789= 43123456789/1000000000.

Where p is equal to 43123456789

And q is equal to 1000000000

If we express q in the form 2m x 5n,

q = 10^9=2^9×5^9=(2×2^8)×(5×5^8)

Where m equal to 2^8 and n is equal to

5^8

(ii)

as this decimal expansion is neither terminating nor recurring decimal expansion it is to be termed as irrational.

(iii)

It is also rational,

for explanation see the first case.

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