Question

multiply
$(2.5 \times 10^{-8}) (9 \times 10^{-10})$
express your answer in scientific notation.
\\(\circ\\) $2.25 \times 10^{-16}$
\\(\circ\\) $2.25 \times 10^{-18}$
\\(\circ\\) $2.25 \times 10^{-17}$
\\(\circ\\) $2.25 \times 10^{-19}$

Explanation:

Step1: Multiply the coefficients

Multiply \(2.5\) and \(9\).
\(2.5\times9 = 22.5\)

Step2: Multiply the powers of 10

Use the rule \(a^m\times a^n=a^{m + n}\) for \(10^{-8}\) and \(10^{-10}\).
\(10^{-8}\times10^{-10}=10^{-8+( - 10)} = 10^{-18}\)

Step3: Combine the results and adjust to scientific notation

We have \(22.5\times10^{-18}\). To write this in scientific notation (where the coefficient is between \(1\) and \(10\)), we rewrite \(22.5\) as \(2.25\times10^{1}\). Then:
\(22.5\times10^{-18}=2.25\times10^{1}\times10^{-18}=2.25\times10^{1+( - 18)} = 2.25\times10^{-17}\)

Answer:

\(2.25\times 10^{-17}\) (corresponding to the option "2.25 × 10⁻¹⁷")