Question
Jed needs to estimate the value of StartFraction 4.32 times 10 Superscript negative 4 Baseline Over 8.71 times 10 Superscript negative 9 Baseline EndFraction. Which statements should he consider? Check all that apply.
4.32 divided by 8.71 is approximately 2.
4.32 divided by 8.71 is approximately 0.5.
The answer will be very small because Negative 4 minus 9 = negative 13.
The number will be large because Negative 4 minus (negative 9) = 5.
He will need to rewrite the preliminary result in scientific notation.
The number will be small because the exponent will be a fraction.
4.32 divided by 8.71 is approximately 2.
4.32 divided by 8.71 is approximately 0.5.
The answer will be very small because Negative 4 minus 9 = negative 13.
The number will be large because Negative 4 minus (negative 9) = 5.
He will need to rewrite the preliminary result in scientific notation.
The number will be small because the exponent will be a fraction.
Answers
GPT-4o mini
To estimate the value of \( \frac{4.32 \times 10^{-4}}{8.71 \times 10^{-9}} \), let's analyze each statement:
1. **4.32 divided by 8.71 is approximately 2.**
- This is **not correct**. In fact, 4.32 divided by 8.71 is closer to 0.5.
2. **4.32 divided by 8.71 is approximately 0.5.**
- This is **correct**. 4.32 is less than half of 8.71, so this approximation is reasonable.
3. **The answer will be very small because Negative 4 minus 9 = negative 13.**
- This is **correct**. When dealing with exponents, \( -4 - 9 = -13 \) means the final result will be multiplied by \( 10^{-13} \), which is a very small number.
4. **The number will be large because Negative 4 minus (negative 9) = 5.**
- This is **not correct**. The calculation \( -4 - (-9) \) does not apply here, and the correct interpretation shows it's a small number, not a large one.
5. **He will need to rewrite the preliminary result in scientific notation.**
- This is **correct**. When dealing with very small numbers, it’s common to express the result in scientific notation for clarity.
6. **The number will be small because the exponent will be a fraction.**
- This is **not correct**. The result will indeed be small because of the negative exponent (-13), not because the exponent is a fraction.
Therefore, the statements Jed should consider are:
- **4.32 divided by 8.71 is approximately 0.5.**
- **The answer will be very small because Negative 4 minus 9 = negative 13.**
- **He will need to rewrite the preliminary result in scientific notation.**
1. **4.32 divided by 8.71 is approximately 2.**
- This is **not correct**. In fact, 4.32 divided by 8.71 is closer to 0.5.
2. **4.32 divided by 8.71 is approximately 0.5.**
- This is **correct**. 4.32 is less than half of 8.71, so this approximation is reasonable.
3. **The answer will be very small because Negative 4 minus 9 = negative 13.**
- This is **correct**. When dealing with exponents, \( -4 - 9 = -13 \) means the final result will be multiplied by \( 10^{-13} \), which is a very small number.
4. **The number will be large because Negative 4 minus (negative 9) = 5.**
- This is **not correct**. The calculation \( -4 - (-9) \) does not apply here, and the correct interpretation shows it's a small number, not a large one.
5. **He will need to rewrite the preliminary result in scientific notation.**
- This is **correct**. When dealing with very small numbers, it’s common to express the result in scientific notation for clarity.
6. **The number will be small because the exponent will be a fraction.**
- This is **not correct**. The result will indeed be small because of the negative exponent (-13), not because the exponent is a fraction.
Therefore, the statements Jed should consider are:
- **4.32 divided by 8.71 is approximately 0.5.**
- **The answer will be very small because Negative 4 minus 9 = negative 13.**
- **He will need to rewrite the preliminary result in scientific notation.**