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

Answer 1

When multiplying two numbers in scientific notation, you follow these steps:

1. Coefficients: Multiply the coefficients together. If you have two numbers in the form \( a \times 10^m \) and \( b \times 10^n \), you would calculate \( a \times b \).

2. Exponents: Add the exponents of the powers of 10. Specifically, you would calculate \( m + n \).

The resulting product will then be in scientific notation, expressed as:

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

For example, if you 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 result is:

\[ 6 \times 10^7 \]