The basic unit of frequency is the hertz, which equals one cycle per second. The inverse of frequency is the period, or the time it takes for one cycle to occur. For example, a frequency of 100 hertz has a period equal to 1/100 second, or 0.01 second. A nanosecond (ns) is one billionth of a second. You can determine the frequency that has a period of 8 ns by finding its inverse.

Express a nanosecond in seconds. One nanosecond is a billionth of a second. A billion is 10 to the ninth power. Write the number 1 and move the decimal nine places to the left. This is one billionth: 0.000000001.

Express 8 nanoseconds in seconds by multiplying the number in Step 1 by 8. This gives you 0.000000008. You can be easily confused by all those decimal places, so check your work with the online Nanoseconds to Seconds Conversion Calculator (see Resources). Enter the number of nanoseconds and instantly read the equivalent number of seconds.

Compute the inverse of the number in Step 2 to obtain the frequency in hertz. You can do this on a calculator by dividing 1 by 0.000000008. Scientific calculators, such as the Online Scientific Calculator (see Resources), commonly include a “1/x” key that does this for you. In the example, 1 divided by 0.000000008 equals 125,000,000. (The calculator may come up with 124,999,999.99999999, but in this case the human has the more accurate answer.)

Check your work using an online tool such as the CalcTool Frequency and period calculator (see Resources). Next to “Input,” change the pull-down to read “ns.” Make sure the units in the next line read “Hz (per s)”. Enter “8” in the “Input” box, click on the “Calculate!” button and read the answer: 1.25000e+8. This is scientific notation for 1.25 times 10 to the eighth power. Move the decimal eight places to the right and you see that the result is 125,000,000 hertz. Your answers agree.

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