Question

If 0.3528 is expressed in the form of p÷2 to the power n and 5 to the power m, find the smallest value of m and n

Answer 1

3528/10000=3528/5⁴*2⁴ 
1764/5⁴*2³ 
882/5⁴*2² 
441/5⁴*2

Answer 2

Answer:

n=1 and m= 4

Step-by-step explanation:

If 0.3528 is expressed in the form of

$\frac{p}{ {2}^{n} \times {5}^{m} }$

then to find the smallest value of m and n, follow these simple steps

$0.3528 \\ \\ = \frac{3528}{10000} \\ \\ = \frac{3528}{ {10}^{4} } \\ \\ = \frac{3528}{ {(2 \times 5)}^{4} } \\ \\ = \frac{3528}{ {2}^{4} \times {5}^{4} }$

but this time the fraction is not standard,because numerator and denominator are not coprime,so

$\frac{1764}{ {5}^{4} \times {2}^{3} } \\ \\ = \frac{882}{ {5}^{4} \times {2}^{2} } \\ \\ = \frac{441}{ {5}^{4} \times 2}$

So, the smallest values of n and m will be 1 and 4 respectively.

Hope you understand