Question

multiply scientific notation quick check

Answer 1

To multiply numbers in scientific notation, you can follow these steps:

1. **Multiply the coefficients**: Multiply the numbers in front of the powers of ten (the coefficients).
2. **Add the exponents**: Add the exponents of the powers of ten.

The general formula is:

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

### Example
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, \((3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7\).

### Practice Problem
Try multiplying \((5 \times 10^2)\) and \((4 \times 10^5)\):

1. **Multiply the coefficients**:
\[
5 \times 4 = 20
\]

2. **Add the exponents**:
\[
2 + 5 = 7
\]

So the answer is:
\[
20 \times 10^7
\]

*Note: \(20 \times 10^7\) can be converted to proper scientific notation as \(2.0 \times 10^8\) (shifting the power to the right).*

Feel free to try another example or let me know if you have any questions!