Question

$\huge\mathfrak\red{hello}$
What can you say about the prime factorisation of the denominators of the rational numbers 0.134 bar ?
PLEASE GUYS ANSWER THIS QUESTION :)

Answer 1

Answer:

0. 134=134/1000

=67/500

500=2^2×5^3

m=2 n=3

please give some thanks.... please.

Answer 2

Answer:

The value of m=2 and n=3.

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

$2^m \times 5^n2 </p><p>m</p><p> ×5 </p><p>n$

?

If yes, write the values of m and n.

Solution :

Rational number 0.134.

Remove decimal to write in fraction,

$0.134=\frac{134}{1000}0.134= </p><p>1000</p><p>134$

Write in simplest form,

$0.134=\frac{67}{500}0.134= </p><p>500</p><p>67$

Now, factories 500

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

$500=2^2\times 5^3500=2 </p><p>2</p><p> ×5 </p><p>3$

So, The denominator is written in the form

$2^m \times 5^n=2^2\times 5^32 </p><p>m</p><p> ×5 </p><p>n</p><p> =2 </p><p>2</p><p> ×5 </p><p>3$

Where, m=2 and n=3

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

I know that.. it is fine not phine... But it's my totla style (⌐■-■)