Question

What can you say about the prime factorization of the denominators of the following
rational numbers?
(1) 43.123456789
(ii) 27.142857
​

Answer 1

Step-by-step explanation:

ANSWER

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