Question

1.) What can you say about the prime factauisation of
the denominators of
the rational number
0.1342​

Answer 1

Answer:

To find : What can you say about the prime factorization of the denominator of the rational number 0.134 when written in the form p/q. Is it of the form 2^m \times 5^n2

m

×5

n

? If yes, write the values of m and n.

Solution :

Rational number 0.134.

Remove decimal to write in fraction,

0.134=\frac{134}{1000}0.134=

1000

134

Write in simplest form,

0.134=\frac{67}{500}0.134=

500

67

Now, factories 500

500=2\times 2\times 5\times 5\times 5500=2×2×5×5×5

500=2^2\times 5^3500=2

2

×5

3

So, The denominator is written in the form 2^m \times 5^n=2^2\times 5^32

m

×5

n

=2

2

×5

3

where, m=2 and n=3

Therefore, The value of m=2 and n=3.