When multiplying two numbers in scientific notation, you perform the following operations:
-
Multiply the Coefficients: Multiply the numerical coefficients (the numbers before the powers of ten).
-
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 \( 2 \times 10^3 \):
- Multiply the coefficients: \( 3 \times 2 = 6 \)
- Add the exponents: \( 4 + 3 = 7 \)
So, the product would be \( 6 \times 10^7 \).