Question

calculate.
$(7 \times 10^3)(6.6 \times 10^2)$
write your answer in scientific notation.

Explanation:

Step1: Multiply the coefficients

Multiply 7 and 6.6: \(7\times6.6 = 46.2\)

Step2: Add the exponents of 10

For \(10^{3}\) and \(10^{2}\), use the rule \(a^{m}\times a^{n}=a^{m + n}\), so \(10^{3}\times10^{2}=10^{3 + 2}=10^{5}\)

Step3: Combine the results

We have \(46.2\times10^{5}\), but in scientific notation, the coefficient should be between 1 and 10. So rewrite 46.2 as \(4.62\times10^{1}\), then multiply by \(10^{5}\): \(4.62\times10^{1}\times10^{5}=4.62\times10^{1 + 5}=4.62\times10^{6}\)

Answer:

\(4.62\times10^{6}\)