Question
Find the quotient of 2.5 × 10-3 and 7.1 × 106. What can be concluded about the solution? Check all that apply.
The E indicates that the solution is given in scientific notation.
The coefficient is 3.5211.
The exponent is 10.
The solution can be written in scientific notation as 3.5211 × 10-10.
The solution is 35,211,000,000.
Answers
Answered by
GPT-4o mini
To find the quotient of \( 2.5 \times 10^{-3} \) and \( 7.1 \times 10^{6} \), we first rewrite the division as follows:
\[
\frac{2.5 \times 10^{-3}}{7.1 \times 10^{6}} = \frac{2.5}{7.1} \times \frac{10^{-3}}{10^{6}}
\]
Now, we calculate each part separately:
1. **Calculating the coefficient**:
\[
\frac{2.5}{7.1} \approx 0.3521126761 \quad (\text{rounded to } 4 \text{ decimal places: } 0.3521)
\]
2. **Calculating the exponents**:
\[
\frac{10^{-3}}{10^{6}} = 10^{-3 - 6} = 10^{-9}
\]
Combining these results, we get:
\[
\frac{2.5 \times 10^{-3}}{7.1 \times 10^{6}} \approx 0.3521 \times 10^{-9}
\]
To express this in scientific notation, we need to adjust the coefficient \( 0.3521 \) to be between 1 and 10. We do this as follows:
\[
0.3521 = 3.521 \times 10^{-1}
\]
So we can rewrite our solution:
\[
0.3521 \times 10^{-9} = 3.521 \times 10^{-1} \times 10^{-9} = 3.521 \times 10^{-10}
\]
Thus, the final answer is:
\[
3.521 \times 10^{-10}
\]
Now, analyzing the conclusions:
1. **The E indicates that the solution is given in scientific notation.**
- **True:** The solution is indeed in scientific notation.
2. **The coefficient is 3.5211.**
- **False:** The coefficient is 3.521 (approximately), not 3.5211.
3. **The exponent is 10.**
- **False:** The exponent is -10.
4. **The solution can be written in scientific notation as 3.5211 × 10^{-10}.**
- **False:** The coefficient obtained is 3.521, so it should be written as \( 3.521 \times 10^{-10} \).
5. **The solution is 35,211,000,000.**
- **False:** The solution in scientific notation is \( 3.521 \times 10^{-10} \), which when converted to decimal notation gives a very small number, specifically \( 0.0000000003521 \).
In summary, the correct conclusions are:
- The E indicates that the solution is given in scientific notation.
\[
\frac{2.5 \times 10^{-3}}{7.1 \times 10^{6}} = \frac{2.5}{7.1} \times \frac{10^{-3}}{10^{6}}
\]
Now, we calculate each part separately:
1. **Calculating the coefficient**:
\[
\frac{2.5}{7.1} \approx 0.3521126761 \quad (\text{rounded to } 4 \text{ decimal places: } 0.3521)
\]
2. **Calculating the exponents**:
\[
\frac{10^{-3}}{10^{6}} = 10^{-3 - 6} = 10^{-9}
\]
Combining these results, we get:
\[
\frac{2.5 \times 10^{-3}}{7.1 \times 10^{6}} \approx 0.3521 \times 10^{-9}
\]
To express this in scientific notation, we need to adjust the coefficient \( 0.3521 \) to be between 1 and 10. We do this as follows:
\[
0.3521 = 3.521 \times 10^{-1}
\]
So we can rewrite our solution:
\[
0.3521 \times 10^{-9} = 3.521 \times 10^{-1} \times 10^{-9} = 3.521 \times 10^{-10}
\]
Thus, the final answer is:
\[
3.521 \times 10^{-10}
\]
Now, analyzing the conclusions:
1. **The E indicates that the solution is given in scientific notation.**
- **True:** The solution is indeed in scientific notation.
2. **The coefficient is 3.5211.**
- **False:** The coefficient is 3.521 (approximately), not 3.5211.
3. **The exponent is 10.**
- **False:** The exponent is -10.
4. **The solution can be written in scientific notation as 3.5211 × 10^{-10}.**
- **False:** The coefficient obtained is 3.521, so it should be written as \( 3.521 \times 10^{-10} \).
5. **The solution is 35,211,000,000.**
- **False:** The solution in scientific notation is \( 3.521 \times 10^{-10} \), which when converted to decimal notation gives a very small number, specifically \( 0.0000000003521 \).
In summary, the correct conclusions are:
- The E indicates that the solution is given in scientific notation.