Question

when multiplying two numbers in scientific notation what operations do you use on the coefficients

Answer 1

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

1. **Multiply the coefficients**: You take the numerical parts (the coefficients) of the scientific notation and multiply them together.

2. **Add the exponents**: You add the exponents of the powers of ten together.

The general formula for multiplying two numbers in scientific notation can be expressed as:

If \( a \times 10^m \) and \( b \times 10^n \) are in scientific notation, then their product is:

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

### Example:

Let’s multiply \( 3.0 \times 10^4 \) and \( 2.0 \times 10^3 \).

1. **Multiply the coefficients**:
\[
3.0 \times 2.0 = 6.0
\]

2. **Add the exponents**:
\[
4 + 3 = 7
\]

Putting it together, the product is:
\[
6.0 \times 10^7
\]

So, \( (3.0 \times 10^4) \times (2.0 \times 10^3) = 6.0 \times 10^7 \).