Question

evaluate the expression without using a calculator. (enter your answer in scientific notation.) \\( \frac{2.5 \times 10^{-4}}{5 \times 10^2} \times 10 \\)

Explanation:

Step1: Simplify the coefficient part

First, we handle the coefficients: $\frac{2.5}{5}$.
$\frac{2.5}{5} = 0.5$

Step2: Simplify the exponent part

For the exponents of 10, we use the rule of exponents $\frac{10^{a}}{10^{b}}=10^{a - b}$ and then multiply by $10$ (which is $10^{1}$).
First, $\frac{10^{-4}}{10^{2}}=10^{-4 - 2}=10^{-6}$, then multiply by $10^{1}$: $10^{-6}\times10^{1}=10^{-6 + 1}=10^{-5}$

Step3: Combine coefficient and exponent

Now we combine the coefficient and the exponent part: $0.5\times10^{-5}$. But in scientific notation, the coefficient should be between 1 and 10, so we rewrite $0.5$ as $5\times10^{-1}$.
Then $5\times10^{-1}\times10^{-5}=5\times10^{-1-5}=5\times10^{-6}$

Answer:

$5\times10^{-6}$