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.
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
GPT-4o mini
To find the quotient of \(2.5 \times 10^{-3}\) and \(7.1 \times 10^{6}\), we can follow these steps:
1. **Divide the coefficients**:
\[
\frac{2.5}{7.1} \approx 0.352112676
\]
2. **Subtract the exponents**:
\[
-3 - 6 = -9
\]
3. **Combine the results**:
\[
0.352112676 \times 10^{-9}
\]
To express this in scientific notation, we need the coefficient to be between 1 and 10, which means we have to adjust the coefficient and the exponent:
1. **Adjust the coefficient**:
\[
0.352112676 = 3.52112676 \times 10^{-1}
\]
2. **Combine with the exponent from the division**:
\[
(3.52112676 \times 10^{-1}) \times 10^{-9} = 3.52112676 \times 10^{-10}
\]
Hence, the final result in scientific notation is:
\[
3.52112676 \times 10^{-10}
\]
Now, let's analyze the statements given in the original question:
1. **The E indicates that the solution is given in scientific notation.**
*True, but it is typically represented with "×" rather than "E". "E" would be in a different format (like \(3.52112676 \times 10^{-10}\) is the same as \(3.52112676E-10\)).*
2. **The coefficient is 3.5211.**
*Not exactly correct. The coefficient is actually approximately \(3.52112676\), which is more than the 4 significant figures given.*
3. **The exponent is 10.**
*False. The exponent is \(-10\).*
4. **The solution can be written in scientific notation as \(3.5211 \times 10^{-10}\).**
*True, if we round to four significant figures.*
5. **The solution is 35,211,000,000.**
*False. This is not in the right form. The correct scientific notation represents a number significantly smaller than this.*
In conclusion, the true statements in the context of your question are:
- The E indicates that the solution is given in scientific notation (though it is more accurate to say it is written in scientific notation using "×").
- The solution can be written in scientific notation as \(3.5211 \times 10^{-10}\).
1. **Divide the coefficients**:
\[
\frac{2.5}{7.1} \approx 0.352112676
\]
2. **Subtract the exponents**:
\[
-3 - 6 = -9
\]
3. **Combine the results**:
\[
0.352112676 \times 10^{-9}
\]
To express this in scientific notation, we need the coefficient to be between 1 and 10, which means we have to adjust the coefficient and the exponent:
1. **Adjust the coefficient**:
\[
0.352112676 = 3.52112676 \times 10^{-1}
\]
2. **Combine with the exponent from the division**:
\[
(3.52112676 \times 10^{-1}) \times 10^{-9} = 3.52112676 \times 10^{-10}
\]
Hence, the final result in scientific notation is:
\[
3.52112676 \times 10^{-10}
\]
Now, let's analyze the statements given in the original question:
1. **The E indicates that the solution is given in scientific notation.**
*True, but it is typically represented with "×" rather than "E". "E" would be in a different format (like \(3.52112676 \times 10^{-10}\) is the same as \(3.52112676E-10\)).*
2. **The coefficient is 3.5211.**
*Not exactly correct. The coefficient is actually approximately \(3.52112676\), which is more than the 4 significant figures given.*
3. **The exponent is 10.**
*False. The exponent is \(-10\).*
4. **The solution can be written in scientific notation as \(3.5211 \times 10^{-10}\).**
*True, if we round to four significant figures.*
5. **The solution is 35,211,000,000.**
*False. This is not in the right form. The correct scientific notation represents a number significantly smaller than this.*
In conclusion, the true statements in the context of your question are:
- The E indicates that the solution is given in scientific notation (though it is more accurate to say it is written in scientific notation using "×").
- The solution can be written in scientific notation as \(3.5211 \times 10^{-10}\).