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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

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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: \[ [8.8] \times 10^{[17]} \, \text{Hz} \]

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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.

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