By Team Aakash Byju's |22nd November 2022
Explain the Prime Factorisations of Denominators of the following numbers. (i) 27.142857 (ii) 43.123456789 (iii) 0.120120012000120000.... (iv) 43.123456789
The number 27.142857 is a type of rational number that is non-terminating but repeating.
Considering 6 decimal digits repeating, we can write it as
27.142857 =
27142857...
10
6
for the first set of 6 decimal digits
=>27.142857 =
27142857...
(2.5)
6
=
27142857...
2 . 5
6
6
=
p
q
Thus, the prime factorisation of the denominator q is of form 2 5 So, the prime factors of the denominator are 2 and 5.
a
b
.
The number 43.123456789 is a terminating decimal with 9 decimal digits. Hence, it is a rational number and can be written in the form of
43.123456789
=
43123456789
10
9
=
43123456789
43123456789
(2.5)
9
10
9
=
=>
=
43123456789
2 . 5
9
9
Thus, the prime factorisation of the denominator q is of form 2 5 So, the prime factors of the denominator are 2 and 5.
.
a
b
The number 0.120120012000120000..... is a non-terminating decimal. Hence, it is not a rational number and cannot be written in the form.
0.120120012000120000 is an Irrational Number.
The number 43.123456789 is a type of rational number that is non-terminating but repeats with 9 decimals.
43.123456789
=
43123456789
10
9
for the first set of 9 decimal digits.
43123456789
43123456789
(2.5)
9
10
=
=>
=
43123456789
2 . 5
9
9
9
Thus, the prime factorisation of the denominator q is of form 2 5 So, the prime factors of the denominator are 2 and 5.
a
b
.