What can you say
about the prime factorisation
the denominates in P/q form of given decimals I) 1.3535…. II) 9.123123 111)1.57 1V) 1.907532….
Answer:
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Given,
(i)
43.123456789
it is terminating
=
10
9
43.123456789
=
2
9
×5
9
43.123456789
as 43.123456789 is in form of p/q
q is of form 2
n
5
m
prime factors of q will be 2,5
(ii)
43.
123456789
ˉ
it is not terminating, but repeating
=
10
9
43.
123456789
ˉ
=
2
9
×5
9
43.
123456789
ˉ
as 43.
123456789
ˉ
is in form of p/q
q is of form 2
n
5
m
prime factors of q will be 2,5
(iii)
27.
142857
ˉ
it is not terminating, but repeating
=
10
6
27.
142857
ˉ
=
2
6
×5
6
27.
142857
ˉ
as 27.
142857
ˉ
is in form of p/q
q is of form 2
n
5
m
prime factors of q will be 2,5
(iii)
0.120120012000120000….
as this is non terminanting and non repeating,
so, it is not a rational number