Question
Compare methods of solving showing similarities and differences:
Alexis
9.3 x 10^7/2.3808 x 10^5
9.3/2.3808 = 3.90625 and 10^7/10^5 = 10^2
3.90625 x 10^2 or 390.625 times larger
Jasmine
93,000,000/238080 = 390.625 times larger
3.90625 x 10^2 in scientific notation
Alexis
9.3 x 10^7/2.3808 x 10^5
9.3/2.3808 = 3.90625 and 10^7/10^5 = 10^2
3.90625 x 10^2 or 390.625 times larger
Jasmine
93,000,000/238080 = 390.625 times larger
3.90625 x 10^2 in scientific notation
Answers
Answered by
GPT-4o mini
Alexis and Jasmine employ different methods to solve the same division of numbers in scientific notation. Here’s a comparison of their techniques, along with the similarities and differences in their approaches:
### Similarities:
1. **Goal**: Both Alexis and Jasmine ultimately aim to calculate the division of \(9.3 \times 10^7\) by \(2.3808 \times 10^5\) and express the result in a meaningful way.
2. **Final Result**: Both methods lead to the same final answer, indicating that the value is \(390.625\) times larger (or \(3.90625 \times 10^2\) in scientific notation).
3. **Focus on Both Numerical and Exponential Parts**: Both methods recognize the importance of treating the numerical part (the coefficients) and the power of ten separately during the calculation.
### Differences:
1. **Methodology**:
- **Alexis** uses the property of scientific notation systematically by dividing the coefficients and using the properties of exponents directly:
- \( \frac{9.3}{2.3808} = 3.90625 \)
- \( \frac{10^7}{10^5} = 10^{7-5} = 10^2 \)
- **Jasmine** simplifies the numbers first by converting them to their full decimal forms before performing the division:
- She computes \( 93,000,000 / 238080 \) to get \(390.625\), then fully converts it to scientific notation afterward.
2. **Step of Conversion**:
- **Alexis** remains in scientific notation throughout, performing calculations with the powers of ten along with the coefficients.
- **Jasmine** transitions from scientific notation to standard decimal form, performing a straightforward division, and then only converts back to scientific notation when stating the final answer.
3. **Intermediate Forms**:
- **Alexis** clearly demonstrates the intermediate result \(3.90625 \times 10^2\) as part of the scientific notation process.
- **Jasmine** gives only the decimal result first and later gives the scientific notation, lacking the intermediate step breakdown related to the powers of ten.
### Conclusion:
Both methods successfully arrive at the same answer, \(3.90625 \times 10^2\) or \(390.625\). Alexis’s approach can be more systematic for work with scientific notation, while Jasmine's method could be quicker for those less comfortable with fractional powers. The choice of method often depends on personal preference and the context of the problem at hand.
### Similarities:
1. **Goal**: Both Alexis and Jasmine ultimately aim to calculate the division of \(9.3 \times 10^7\) by \(2.3808 \times 10^5\) and express the result in a meaningful way.
2. **Final Result**: Both methods lead to the same final answer, indicating that the value is \(390.625\) times larger (or \(3.90625 \times 10^2\) in scientific notation).
3. **Focus on Both Numerical and Exponential Parts**: Both methods recognize the importance of treating the numerical part (the coefficients) and the power of ten separately during the calculation.
### Differences:
1. **Methodology**:
- **Alexis** uses the property of scientific notation systematically by dividing the coefficients and using the properties of exponents directly:
- \( \frac{9.3}{2.3808} = 3.90625 \)
- \( \frac{10^7}{10^5} = 10^{7-5} = 10^2 \)
- **Jasmine** simplifies the numbers first by converting them to their full decimal forms before performing the division:
- She computes \( 93,000,000 / 238080 \) to get \(390.625\), then fully converts it to scientific notation afterward.
2. **Step of Conversion**:
- **Alexis** remains in scientific notation throughout, performing calculations with the powers of ten along with the coefficients.
- **Jasmine** transitions from scientific notation to standard decimal form, performing a straightforward division, and then only converts back to scientific notation when stating the final answer.
3. **Intermediate Forms**:
- **Alexis** clearly demonstrates the intermediate result \(3.90625 \times 10^2\) as part of the scientific notation process.
- **Jasmine** gives only the decimal result first and later gives the scientific notation, lacking the intermediate step breakdown related to the powers of ten.
### Conclusion:
Both methods successfully arrive at the same answer, \(3.90625 \times 10^2\) or \(390.625\). Alexis’s approach can be more systematic for work with scientific notation, while Jasmine's method could be quicker for those less comfortable with fractional powers. The choice of method often depends on personal preference and the context of the problem at hand.