Question

calculate.
(3×10⁻³)(4.7×10⁻⁷)
write your answer in scientific notation.

Explanation:

Step1: Multiply coefficients

Multiply 3 and 4.7: \(3\times4.7 = 14.1\)

Step2: Add exponents of 10

For \(10^{-3}\) and \(10^{-7}\), add exponents: \(-3 + (-7)=-10\), so \(10^{-3}\times10^{-7}=10^{-10}\)

Step3: Combine results

We have \(14.1\times10^{-10}\), but scientific notation requires coefficient between 1 - 10. Rewrite 14.1 as \(1.41\times10^{1}\), then multiply by \(10^{-10}\): \(1.41\times10^{1}\times10^{-10}=1.41\times10^{-9}\)

Answer:

\(1.41\times10^{-9}\)