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

Question

1. Add the coefficients and multiply the exponents of the powers of 10.
2. Add the coefficients and add the exponents of the powers of 10.
3. Multiply the coefficients and add the exponents of the powers of 10.
4. Multiply the coefficients and multiply the exponents of the powers of 10.

Answer 1

When multiplying two numbers in scientific notation, you should:

3. Multiply the coefficients and add the exponents of the powers of 10.

For example, if you have \( (a \times 10^m) \) and \( (b \times 10^n) \), when you multiply them, you calculate it as follows:

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

So, you multiply the coefficients \( a \) and \( b \), and you add the exponents \( m \) and \( n \).