Question
How many hertz are in a UV light with a frequency of \( 8.8 \times 10^{11} \mathrm{MHz} \) ? Give your answer in proper scientific notation. \[ [?] \times 10^{[?]} \mathrm{Hz} \] Enter the coefficient in the green box and the exponent in the yellow box.
Ask by Murphy Davey. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The frequency of the UV light is \( 8.8 \times 10^{17} \, \text{Hz} \).
Solution
To convert the frequency from megahertz (MHz) to hertz (Hz), we need to remember that:
1 MHz = \( 10^6 \) Hz.
Given the frequency of UV light is \( 8.8 \times 10^{11} \) MHz, we can convert it to Hz as follows:
\[
\text{Frequency in Hz} = 8.8 \times 10^{11} \, \text{MHz} \times 10^6 \, \text{Hz/MHz}
\]
Now, let's perform the calculation:
\[
\text{Frequency in Hz} = 8.8 \times 10^{11} \times 10^6 = 8.8 \times 10^{11 + 6} = 8.8 \times 10^{17} \, \text{Hz}
\]
Thus, the frequency of the UV light in hertz is \( 8.8 \times 10^{17} \, \text{Hz} \).
In proper scientific notation, the answer is:
- Coefficient: \( 8.8 \)
- Exponent: \( 17 \)
So, the final answer is:
\[
[8.8] \times 10^{[17]} \, \text{Hz}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain
Simplify this solution
Bonus Knowledge
To convert megahertz (MHz) to hertz (Hz), you can use the fact that \(1 \, \text{MHz} = 10^6 \, \text{Hz}\). Given the frequency of UV light is \(8.8 \times 10^{11} \, \text{MHz}\): 1. Convert to Hz: \[ 8.8 \times 10^{11} \, \text{MHz} \times 10^6 \, \text{Hz/MHz} = 8.8 \times 10^{11 + 6} \, \text{Hz} \] 2. Simplifying the exponent: \[ = 8.8 \times 10^{17} \, \text{Hz} \] So, the final answer in proper scientific notation is: \[ 8.8 \times 10^{17} \mathrm{Hz} \] Enter the coefficient \( 8.8 \) in the green box and the exponent \( 17 \) in the yellow box.