Question
Aubrey says that the product of 104 and 10–2 is 10–8. Is she correct? If not, explain why.
Yes, she is correct.
No, the exponent should be positive 8.
No, she multiplied the exponents instead of adding them.
No, she multiplied the exponents instead of subtracting them.
Yes, she is correct.
No, the exponent should be positive 8.
No, she multiplied the exponents instead of adding them.
No, she multiplied the exponents instead of subtracting them.
Answers
GPT-4o mini
To determine if Aubrey is correct, let's first calculate the product of 104 and 10^(-2).
The expression can be simplified as follows:
\[
104 \times 10^{-2} = 104 \times \frac{1}{10^2} = 104 \times \frac{1}{100} = 1.04
\]
In scientific notation, \( 1.04 \) can be expressed as \( 1.04 \times 10^0 \) (since \( 10^0 = 1 \)).
Now let's analyze what she claimed. Aubrey said that:
\[
104 \times 10^{-2} = 10^{-8}
\]
This is incorrect, as \( 10^{-8} \) represents a much smaller number than \( 1.04 \).
Therefore, she is not correct. The correct answer among the provided options is:
**No, the exponent should be positive 8.**
This would be correct if we were considering \( 104 \times 10^8 \), but in the context of her statement, the reasoning is that her result was incorrect overall. However, the best specific answer related to her mistake is that she didn’t properly manipulate the powers of ten, leading to confusion. Thus the best precise option is:
**No, she multiplied the exponents instead of subtracting them.**
Although she hasn't explicitly calculated powers, her statement about exponents in that context is indeed incorrect based on the multiplication of scientific numbers.
The expression can be simplified as follows:
\[
104 \times 10^{-2} = 104 \times \frac{1}{10^2} = 104 \times \frac{1}{100} = 1.04
\]
In scientific notation, \( 1.04 \) can be expressed as \( 1.04 \times 10^0 \) (since \( 10^0 = 1 \)).
Now let's analyze what she claimed. Aubrey said that:
\[
104 \times 10^{-2} = 10^{-8}
\]
This is incorrect, as \( 10^{-8} \) represents a much smaller number than \( 1.04 \).
Therefore, she is not correct. The correct answer among the provided options is:
**No, the exponent should be positive 8.**
This would be correct if we were considering \( 104 \times 10^8 \), but in the context of her statement, the reasoning is that her result was incorrect overall. However, the best specific answer related to her mistake is that she didn’t properly manipulate the powers of ten, leading to confusion. Thus the best precise option is:
**No, she multiplied the exponents instead of subtracting them.**
Although she hasn't explicitly calculated powers, her statement about exponents in that context is indeed incorrect based on the multiplication of scientific numbers.