Question

What can you say about the prime factorisation of the denominator of the rational number 0.134 when written in the form p/q. Is it of the form 2^m x 5^n? If yes, write the values of m and n

Answer 1

0.134 = 134/1000
   = 67/500
denom = 500 = 5 * 2 * 5 * 2 * 5 = 5³ * 2²

m = 2    n = 3

Answer 2

Answer:

The value of m=2 and n=3.

Step-by-step explanation:

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 $2^m \times 5^n$? If yes, write the values of m and n.

Solution :

Rational number 0.134.

Remove decimal to write in fraction,

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

Write in simplest form,

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

Now, factories 500

$500=2\times 2\times 5\times 5\times 5$

$500=2^2\times 5^3$

So, The denominator is written in the form $2^m \times 5^n=2^2\times 5^3$

where, m=2 and n=3

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