Question

Explain the steps you would take to find the product of 6.7 × 106 and 3.2 × 105 written in scientific notation.

write one paragraph

Answer 1

To find the product of \(6.7 \times 10^6\) and \(3.2 \times 10^5\) in scientific notation, start by multiplying the coefficients (the numbers in front of the powers of ten). Multiply \(6.7\) by \(3.2\) to get \(21.44\). Next, add the exponents of the powers of ten: \(6\) (from \(10^6\)) plus \(5\) (from \(10^5\)) equals \(11\). So, the multiplication yields \(21.44 \times 10^{11}\). Since \(21.44\) is not in proper scientific notation (where the coefficient must be between \(1\) and \(10\)), convert it by rewriting \(21.44\) as \(2.144 \times 10^1\). Now, combine this with \(10^{11}\) by adding the exponents: \(1 + 11 = 12\), resulting in \(2.144 \times 10^{12}\). Therefore, the product of \(6.7 \times 10^6\) and \(3.2 \times 10^5\) in scientific notation is \(2.144 \times 10^{12}\).