Question
Use scientific notation to find the product of 7.13 × 10^-3 and 40. Include all of your calculations in your final answer.
Answers
GPT-4o mini
To find the product of \( 7.13 \times 10^{-3} \) and \( 40 \), we can follow these steps:
1. **Multiply the coefficients**:
The coefficients are \( 7.13 \) and \( 40 \).
\[
7.13 \times 40 = 285.2
\]
2. **Combine with the power of ten**:
Since \( 7.13 \times 10^{-3} \) includes \( 10^{-3} \), we have:
\[
285.2 \times 10^{-3}
\]
3. **Convert to scientific notation**:
To convert \( 285.2 \) to scientific notation, we write it as \( 2.852 \times 10^2 \) (since we move the decimal point two places to the left).
4. **Combine the powers of ten**:
Now we can rewrite our previous product:
\[
285.2 \times 10^{-3} = 2.852 \times 10^2 \times 10^{-3}
\]
When multiplying powers of ten, we add the exponents:
\[
10^{2 + (-3)} = 10^{-1}
\]
5. **Final result**:
Therefore, combining everything, we get:
\[
2.852 \times 10^{-1}
\]
Thus, the final answer in scientific notation is:
\[
\boxed{2.852 \times 10^{-1}}
\]
1. **Multiply the coefficients**:
The coefficients are \( 7.13 \) and \( 40 \).
\[
7.13 \times 40 = 285.2
\]
2. **Combine with the power of ten**:
Since \( 7.13 \times 10^{-3} \) includes \( 10^{-3} \), we have:
\[
285.2 \times 10^{-3}
\]
3. **Convert to scientific notation**:
To convert \( 285.2 \) to scientific notation, we write it as \( 2.852 \times 10^2 \) (since we move the decimal point two places to the left).
4. **Combine the powers of ten**:
Now we can rewrite our previous product:
\[
285.2 \times 10^{-3} = 2.852 \times 10^2 \times 10^{-3}
\]
When multiplying powers of ten, we add the exponents:
\[
10^{2 + (-3)} = 10^{-1}
\]
5. **Final result**:
Therefore, combining everything, we get:
\[
2.852 \times 10^{-1}
\]
Thus, the final answer in scientific notation is:
\[
\boxed{2.852 \times 10^{-1}}
\]
can you make it a little less advanced and without all the symbols and slashes
GPT-4o mini
Sure! Let's break it down step by step without using too many symbols.
1. **Start by multiplying the numbers**: We have 7.13 and 40.
- When you multiply 7.13 by 40, you get 285.2.
2. **Attach the power of ten**: Since we started with 7.13 times 10 to the power of -3, we now need to deal with that.
- So, we write it as 285.2 times 10 to the power of -3.
3. **Convert 285.2 into scientific notation**: We need to express 285.2 in scientific notation.
- In scientific notation, 285.2 is written as 2.852 times 10 to the power of 2. (We move the decimal point two places to the left).
4. **Combine the powers of ten**: Now, we have 2.852 times 10 to the power of 2 and we still have our original 10 to the power of -3.
- You add the exponents when combining powers of ten. So, 2 plus -3 gives us -1.
5. **Final answer**: Putting this all together, we get:
- 2.852 times 10 to the power of -1.
So, the final answer in scientific notation is 2.852 times 10 to the power of -1.
1. **Start by multiplying the numbers**: We have 7.13 and 40.
- When you multiply 7.13 by 40, you get 285.2.
2. **Attach the power of ten**: Since we started with 7.13 times 10 to the power of -3, we now need to deal with that.
- So, we write it as 285.2 times 10 to the power of -3.
3. **Convert 285.2 into scientific notation**: We need to express 285.2 in scientific notation.
- In scientific notation, 285.2 is written as 2.852 times 10 to the power of 2. (We move the decimal point two places to the left).
4. **Combine the powers of ten**: Now, we have 2.852 times 10 to the power of 2 and we still have our original 10 to the power of -3.
- You add the exponents when combining powers of ten. So, 2 plus -3 gives us -1.
5. **Final answer**: Putting this all together, we get:
- 2.852 times 10 to the power of -1.
So, the final answer in scientific notation is 2.852 times 10 to the power of -1.