How many hertz are in a yellow light with a frequency of [tex]$5.2 \times 10^8 MHz$[/tex]? Give your answer in proper scientific notation. [?] [tex]$\times 10^{[?]} Hz$[/tex]
Answer (2)
Convert MHz to Hz by multiplying by 1 0 6 .
Multiply 5.2 × 1 0 8 by 1 0 6 to get 5.2 × 1 0 14 .
The frequency in Hz is 5.2 × 1 0 14 Hz .
The final answer in scientific notation is 5.2 × 1 0 14 Hz .
Explanation
Understanding the Problem We are given the frequency of yellow light as 5.2 × 1 0 8 MHz and we need to convert this to hertz (Hz). We also need to express the final answer in scientific notation.
Conversion Factor First, we need to know the conversion factor between MHz and Hz. We know that 1 MHz (megahertz) is equal to 1 0 6 Hz (hertz).
Converting MHz to Hz To convert the given frequency from MHz to Hz, we multiply the frequency in MHz by the conversion factor 1 0 6 . So, we have:
5.2 × 1 0 8 M Hz × 1 0 6 M Hz Hz = 5.2 × 1 0 ( 8 + 6 ) Hz = 5.2 × 1 0 14 Hz
Final Answer The frequency of the yellow light in hertz is 5.2 × 1 0 14 Hz . This is already in scientific notation, so we can directly provide the answer in the requested format.
Examples
Understanding frequency conversions is crucial in many fields, such as telecommunications, where different frequency bands are used for various applications like radio, television, and mobile communication. For example, converting the frequency of a radio signal from MHz to Hz helps engineers design and optimize receiver circuits. Similarly, in medical imaging, understanding the frequencies of electromagnetic waves used in MRI or X-ray machines is essential for accurate diagnosis and treatment. This conversion skill ensures accurate measurements and compatibility across different systems and technologies.
The frequency of yellow light of 5.2 × 1 0 8 MHz converts to 5.2 × 1 0 14 Hz when using the conversion factor of 1 0 6 Hz per MHz. This result is in proper scientific notation. Thus, the answer is 5.2 × 1 0 14 Hz .
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