Question
What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply. 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
To analyze the statements regarding the quotient in scientific notation, let's go through each conclusion one by one:
1. **The coefficient of the solution is 6.4, the difference of the original coefficients.**
- This statement can be true in some cases. When dividing coefficients, you actually perform the division of the coefficients. If the original coefficients were, for example, 8.0 and 1.25, dividing those would give you a coefficient somewhere between 1 and 10, not necessarily 6.4. Hence, without specific original values provided, this statement cannot always be true.
2. **The exponent of the solution is –12, the difference of the original exponents.**
- This statement is true. When dividing numbers in scientific notation, you subtract the exponent in the denominator from the exponent in the numerator. So if you had an exponent of -10 divided by an exponent of -2, you would subtract: -10 - (-2) = -10 + 2 = -8.
3. **The coefficient of the solution must be greater than or equal to one but less than 10.**
- This statement is true. By convention, in scientific notation, the coefficient (the number in front) must be between 1 and 10. If the coefficient falls outside this range after performing the division, it would need to be adjusted appropriately.
4. **The quotient is 3.0 × 10^-12.**
- This could be true if the specific values used for the division resulted in that output. Without knowing the original values, we can't definitively accept or deny this statement. However, if the calculations led to that exact result, then it is accurate.
5. **The solution is a very large number.**
- The statement "very large number" is relative. A number given in scientific notation such as \( 3.0 \times 10^{-12} \) is actually a very small number, since it is less than 1. So this statement is false.
### Conclusion:
From the statements provided, we can conclude the following:
- The exponent of the solution is accurately the difference of the original exponents (True).
- The coefficient of the solution must be between 1 and 10 (True).
- The statements about specific coefficients and the representation of "very large" require context but can't be universally claimed to be true (False or uncertain).
Thus, the reliable statements to check are the ones related to coefficients and exponents in scientific notation, while being cautious about specific values and the term "very large."
1. **The coefficient of the solution is 6.4, the difference of the original coefficients.**
- This statement can be true in some cases. When dividing coefficients, you actually perform the division of the coefficients. If the original coefficients were, for example, 8.0 and 1.25, dividing those would give you a coefficient somewhere between 1 and 10, not necessarily 6.4. Hence, without specific original values provided, this statement cannot always be true.
2. **The exponent of the solution is –12, the difference of the original exponents.**
- This statement is true. When dividing numbers in scientific notation, you subtract the exponent in the denominator from the exponent in the numerator. So if you had an exponent of -10 divided by an exponent of -2, you would subtract: -10 - (-2) = -10 + 2 = -8.
3. **The coefficient of the solution must be greater than or equal to one but less than 10.**
- This statement is true. By convention, in scientific notation, the coefficient (the number in front) must be between 1 and 10. If the coefficient falls outside this range after performing the division, it would need to be adjusted appropriately.
4. **The quotient is 3.0 × 10^-12.**
- This could be true if the specific values used for the division resulted in that output. Without knowing the original values, we can't definitively accept or deny this statement. However, if the calculations led to that exact result, then it is accurate.
5. **The solution is a very large number.**
- The statement "very large number" is relative. A number given in scientific notation such as \( 3.0 \times 10^{-12} \) is actually a very small number, since it is less than 1. So this statement is false.
### Conclusion:
From the statements provided, we can conclude the following:
- The exponent of the solution is accurately the difference of the original exponents (True).
- The coefficient of the solution must be between 1 and 10 (True).
- The statements about specific coefficients and the representation of "very large" require context but can't be universally claimed to be true (False or uncertain).
Thus, the reliable statements to check are the ones related to coefficients and exponents in scientific notation, while being cautious about specific values and the term "very large."