Math, asked by uzairnafees915, 1 month ago

what is rational numbers in given this below (I) 43.123456789,(II) 0.12012001200012000, (III) 0, (Iv) 3/2​​

Answers

Answered by stuti512
0

Answer:

option d

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Answered by shivanisharma93277
0

Answer:

Answer

i) 43.123456789 is terminating or rational

43.123456789=

1000000000

43123456789

=

10

9

43123456789

=

(2×5)

9

43123456789

=

2

9

×5

9

43123456789

This is in the form of

q

p

, and the prime factors of q are in terms of 2 and 5.

ii) 0.120120012000120000.... is non-terminating and non-repeating, it is irrational. Hence cannot be expressed in the form of

q

p

iii) 43.

123456789

is non-terminating but repeating. So, it would be rational.

Let x=43.

123456789

…(1)

1000000000x=43123456789,

123456789

…(2)

(2)−(1)⇒999999999x=43123456746⇒x=

999999999

43123456746

=

3

4

×37

1

×333667

1

43123456746

In a non-termination repeating expansion of

q

p

, q will have factors 3,37,333667.

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