Question
What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply.
StartFraction (9.6 times 10 Superscript negative 8 Baseline) Over (3.2 times 10 Superscript 4 Baseline) EndFraction
The coefficient of the solution is 6.4, the difference of the original coefficients.
The exponent of the solution is –12, the difference of the original exponents.
The coefficient of the solution must be greater than or equal to one but less than 10.
The quotient is 3.0 × 10-12
The solution is a very large number.
StartFraction (9.6 times 10 Superscript negative 8 Baseline) Over (3.2 times 10 Superscript 4 Baseline) EndFraction
The coefficient of the solution is 6.4, the difference of the original coefficients.
The exponent of the solution is –12, the difference of the original exponents.
The coefficient of the solution must be greater than or equal to one but less than 10.
The quotient is 3.0 × 10-12
The solution is a very large number.
Answers
Answered by
GPT-4o mini
Let's break down the problem step by step to determine which conclusions can be drawn regarding the quotient of the given expression in scientific notation:
Given:
\[
\frac{9.6 \times 10^{-8}}{3.2 \times 10^{4}}
\]
1. **Coefficients Division**:
- Divide the coefficients:
\[
\frac{9.6}{3.2} = 3.0
\]
- So, the coefficient of the solution is 3.0, not 6.4.
2. **Exponents Subtraction**:
- Subtract the exponents:
\[
-8 - 4 = -12
\]
- So, the exponent of the solution is indeed -12.
3. **Coefficient Condition**:
- In scientific notation, the coefficient must be greater than or equal to 1 but less than 10. The coefficient we found is 3.0, which satisfies this condition.
4. **Combining Coefficient and Exponent**:
- Therefore, the quotient can be expressed as:
\[
3.0 \times 10^{-12}
\]
5. **Magnitude of the Solution**:
- A number in scientific notation with a negative exponent indicates a very small number. Hence, \(3.0 \times 10^{-12}\) is a very small number, not a very large number.
**Conclusion Summary**:
- The coefficient of the solution is 3.0, **not** 6.4.
- The exponent of the solution is -12, which is correct.
- The coefficient of the solution is indeed between 1 and 10 (3.0).
- The quotient is \(3.0 \times 10^{-12}\).
- The solution is **not** a very large number; it is a very small number.
**Correct answers**:
- The exponent of the solution is –12, the difference of the original exponents.
- The coefficient of the solution must be greater than or equal to one but less than 10.
- The quotient is \(3.0 \times 10^{-12}\).
Given:
\[
\frac{9.6 \times 10^{-8}}{3.2 \times 10^{4}}
\]
1. **Coefficients Division**:
- Divide the coefficients:
\[
\frac{9.6}{3.2} = 3.0
\]
- So, the coefficient of the solution is 3.0, not 6.4.
2. **Exponents Subtraction**:
- Subtract the exponents:
\[
-8 - 4 = -12
\]
- So, the exponent of the solution is indeed -12.
3. **Coefficient Condition**:
- In scientific notation, the coefficient must be greater than or equal to 1 but less than 10. The coefficient we found is 3.0, which satisfies this condition.
4. **Combining Coefficient and Exponent**:
- Therefore, the quotient can be expressed as:
\[
3.0 \times 10^{-12}
\]
5. **Magnitude of the Solution**:
- A number in scientific notation with a negative exponent indicates a very small number. Hence, \(3.0 \times 10^{-12}\) is a very small number, not a very large number.
**Conclusion Summary**:
- The coefficient of the solution is 3.0, **not** 6.4.
- The exponent of the solution is -12, which is correct.
- The coefficient of the solution is indeed between 1 and 10 (3.0).
- The quotient is \(3.0 \times 10^{-12}\).
- The solution is **not** a very large number; it is a very small number.
**Correct answers**:
- The exponent of the solution is –12, the difference of the original exponents.
- The coefficient of the solution must be greater than or equal to one but less than 10.
- The quotient is \(3.0 \times 10^{-12}\).