when multiplying two numbers in scientific notation, what operations do you use on the coefficients and the exponents to the powers of 10?

Answer 1

When multiplying two numbers in scientific notation, you perform the following operations:

1. Multiply the Coefficients: Multiply the numerical coefficients (the numbers before the powers of ten).

2. Add the Exponents: Add the exponents of the powers of ten.

In mathematical terms, if you have two numbers in scientific notation, \( a \times 10^m \) and \( b \times 10^n \), their product is given by:

\[ (a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{(m+n)} \]

For example, if you want to multiply \( 3 \times 10^4 \) and \( 2 \times 10^3 \):

1. Multiply the coefficients: \( 3 \times 2 = 6 \)
2. Add the exponents: \( 4 + 3 = 7 \)

So, the product would be \( 6 \times 10^7 \).