How many hertz are in 96 megahertz? Express the answer in correct scientific notation. [tex]$96 MHz=[?] \times 10^{[?]} Hz$[/tex]
Enter the coefficient in the green box and the exponent in the yellow box.
Answer (1)
Convert MHz to Hz: 96 MHz = 96 × 1 0 6 Hz .
Calculate the result: 96 × 1 0 6 = 96 , 000 , 000 Hz .
Express in scientific notation: 96 , 000 , 000 = 9.6 × 1 0 7 .
The answer is 9.6 × 1 0 7 .
Explanation
Understanding the Problem We are asked to convert 96 megahertz (MHz) to hertz (Hz) and express the result in scientific notation. We know that 1 MHz is equal to 1 0 6 Hz.
Conversion To convert 96 MHz to Hz, we multiply 96 by 1 0 6 :
96 MHz = 96 × 1 0 6 Hz = 96 , 000 , 000 Hz
Scientific Notation Now, we need to express 96,000,000 in scientific notation, which is in the form a × 1 0 b , where 1 ≤ a < 10 and b is an integer. To do this, we can rewrite 96,000,000 as 9.6 × 1 0 7 .
Final Answer Therefore, 96 MHz is equal to 9.6 × 1 0 7 Hz.
Examples
Scientific notation is useful in many fields, such as physics and engineering, to represent very large or very small numbers. For example, the speed of light is approximately 3 × 1 0 8 meters per second, and the size of an atom is approximately 1 × 1 0 − 10 meters. Using scientific notation makes it easier to work with these numbers and compare their magnitudes. In computer science, we often use prefixes like mega (M) and giga (G) to denote large numbers of bytes. Converting between these units often involves scientific notation.
