what is rational numbers in given this below (I) 43.123456789,(II) 0.12012001200012000, (III) 0, (Iv) 3/2
Answers
Answer:
option d
please follow
me and mark me as brainlist
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.