Question
When multiplying two numbers in scientific notation
Answers
GPT-4o mini
When multiplying two numbers in scientific notation, you should follow these steps:
1. **Multiply the coefficients**: Take the coefficients (the numbers in front) and multiply them together.
2. **Add the exponents**: Take the exponents of the powers of ten and add them together.
3. **Combine the results**: Combine the new coefficient and the new exponent to write the result in scientific notation.
### Example:
Let's multiply \( (3.2 \times 10^4) \) and \( (2.5 \times 10^3) \).
1. **Multiply the coefficients**:
\[
3.2 \times 2.5 = 8.0
\]
2. **Add the exponents**:
\[
4 + 3 = 7
\]
3. **Combine the results**:
The result in scientific notation is:
\[
8.0 \times 10^7
\]
### Adjusting to Proper Scientific Notation:
Make sure the coefficient is between 1 and 10. In this case, \( 8.0 \) is fine.
Thus, the final result is:
\[
8.0 \times 10^7
\]
1. **Multiply the coefficients**: Take the coefficients (the numbers in front) and multiply them together.
2. **Add the exponents**: Take the exponents of the powers of ten and add them together.
3. **Combine the results**: Combine the new coefficient and the new exponent to write the result in scientific notation.
### Example:
Let's multiply \( (3.2 \times 10^4) \) and \( (2.5 \times 10^3) \).
1. **Multiply the coefficients**:
\[
3.2 \times 2.5 = 8.0
\]
2. **Add the exponents**:
\[
4 + 3 = 7
\]
3. **Combine the results**:
The result in scientific notation is:
\[
8.0 \times 10^7
\]
### Adjusting to Proper Scientific Notation:
Make sure the coefficient is between 1 and 10. In this case, \( 8.0 \) is fine.
Thus, the final result is:
\[
8.0 \times 10^7
\]