Question

question
what is the product of $2.8 \times 10^3$ and $9.7 \times 10^3$ expressed in scientific notation?
answer attempt 1 out of 2
answer: $\square \times 10^{\square}$

Explanation:

Step1: Multiply the coefficients

Multiply \(2.8\) and \(9.7\).
\(2.8\times9.7 = 27.16\)

Step2: Multiply the powers of 10

Use the rule \(a^m\times a^n=a^{m + n}\) for \(10^3\times10^3\).
\(10^3\times10^3=10^{3 + 3}=10^6\)

Step3: Combine the results and adjust to scientific notation

We have \(27.16\times10^6\), but in scientific notation, the coefficient should be between \(1\) and \(10\). So we rewrite \(27.16\) as \(2.716\times10^1\). Then multiply by \(10^6\):
\(2.716\times10^1\times10^6 = 2.716\times10^{1+6}=2.716\times10^7\)

Answer:

\(2.716\times10^{7}\)