Question
The speed of light is approximately 3 cross times 10 to the power of 8 meters per second. While solving a problem, Cara used 3 cross times 10 to the power of 10 meters per second for the speed of light and got the incorrect answer. By which factor should Cara multiply her answer in order to get the correct answer?
10 to the power of minus 18 end exponent
10 to the power of minus 2 end exponent
10 to the power of 2
10 to the power of 18
10 to the power of minus 18 end exponent
10 to the power of minus 2 end exponent
10 to the power of 2
10 to the power of 18
Answers
GPT-4o mini
To determine the factor by which Cara should multiply her incorrect answer to get the correct answer, we first need to compare the speed values she used and the actual speed of light.
1. **Actual speed of light (c):** \( 3 \times 10^8 \) meters per second
2. **Incorrect speed used by Cara:** \( 3 \times 10^{10} \) meters per second
Next, we find the ratio of the correct speed to the incorrect speed:
\[
\text{Factor} = \frac{\text{Actual speed}}{\text{Incorrect speed}} = \frac{3 \times 10^8}{3 \times 10^{10}}
\]
We can simplify this:
\[
\text{Factor} = \frac{3 \times 10^8}{3 \times 10^{10}} = \frac{10^8}{10^{10}} = 10^{8-10} = 10^{-2}
\]
This means that to correct her answer, Cara should multiply her result by \( 10^{-2} \).
Thus, the answer is:
**10 to the power of minus 2 end exponent**
1. **Actual speed of light (c):** \( 3 \times 10^8 \) meters per second
2. **Incorrect speed used by Cara:** \( 3 \times 10^{10} \) meters per second
Next, we find the ratio of the correct speed to the incorrect speed:
\[
\text{Factor} = \frac{\text{Actual speed}}{\text{Incorrect speed}} = \frac{3 \times 10^8}{3 \times 10^{10}}
\]
We can simplify this:
\[
\text{Factor} = \frac{3 \times 10^8}{3 \times 10^{10}} = \frac{10^8}{10^{10}} = 10^{8-10} = 10^{-2}
\]
This means that to correct her answer, Cara should multiply her result by \( 10^{-2} \).
Thus, the answer is:
**10 to the power of minus 2 end exponent**