Question

which shows the expression below simplified?
$(8 \times 10^5) \times 0.0005$
\\(\bigcirc\\) a. \\(1.3 \times 10^{-20}\\)
\\(\bigcirc\\) b. \\(4 \times 10^2\\)
\\(\bigcirc\\) c. \\(4 \times 10^{-20}\\)

Explanation:

Step1: Convert 0.0005 to scientific notation

0.0005 can be written as \(5\times10^{-4}\) because we move the decimal point 4 places to the right to get a number between 1 and 10.

Step2: Multiply the coefficients and the powers of 10 separately

First, multiply the coefficients: \(8\times5 = 40\).
Then, multiply the powers of 10: \(10^{5}\times10^{-4}=10^{5 + (-4)}=10^{1}\) (using the rule \(a^{m}\times a^{n}=a^{m + n}\)).

Step3: Combine the results and simplify

We have \(40\times10^{1}\). But in scientific notation, the coefficient should be between 1 and 10. So we rewrite 40 as \(4\times10^{1}\). Then, \(4\times10^{1}\times10^{1}=4\times10^{1 + 1}=4\times10^{2}\) (again using the rule for multiplying powers of 10).

Answer:

B. \(4\times10^{2}\)