Why Use Microseconds Instead of Nanoseconds in Engineering Calculations?

[marly]

I’m taking an electronics course and in the book it’s talking about a period in AC electricity and it asking me to find the frequency for the period and also the time for the frequency.

The problem is this:

Calculate the period for the two frequencies of 1 MHz and 2 MHz.

For 1 MHz I use T = $\frac{1}{f}$ = $\frac{1}{1 x 10^{6}}$ = 1 x 10$^{-6}$ = 1 $\mu$s

This makes sense to me and when I put it in my calculator I get 1 x 10 $^{-6}$

For 2MHz in the book it shows:

For 2 MHz I use T = $\frac{1}{f}$ = $\frac{1}{2 x 10^{6}}$ = .5 x 10$^{-6}$ = .5 $\mu$s

This answer makes sense to me too.

On my calculator it shows 500 x $^{-9}$ which is 500 nanoseconds, instead of .5 microseconds.

What I don't understand, is why would I use .5 $\mu$s instead of 500 nanoseconds?

To me, it would seem more "right" to say, "oh, that's 500 nanoseconds, instead of .5 microseconds".

 

[SteamKing]

Engineering notation is a special form of scientific notation, where the number is expressed such that the exponent of ten is some multiple (positive or negative) of 3.

For more details, see:
https://www.dlsweb.rmit.edu.au/lsu/content/3_MathsEssentials/maths_pdfs/scientific%20notation.pdf

 

[phyzguy]

Technically, in engineering notation, the number before the unit should always be between 1.0 and 1000.0. So instead of saying 0.5 microsecond, you should say 500 nanosecond. If you went to shorter and shorter times, you would keep using ns until you got to 1.0 ns, and below that you would say 990 picosecond instead of 0.99 ns. However, there is nothing wrong with saying 0.5 microsecond, and I doubt you would get marked down for giving this answer.

 

[marly]

Thank you very much. That makes sense perfect sense. Thanks!

My book says the answer is .5 microseconds and that’s why I was getting confused. I thought the answer should have been 500 nanoseconds, because as you said, the number before the unit should be 1.0 and 1000.0

 

[rezeew]

I can understand your confusion with the units used in this problem. However, it is important to understand that engineering notation is used to express very large or very small numbers in a more convenient and concise way. In this case, the frequency is given in megahertz (MHz), which is equivalent to 1 million hertz (Hz). Therefore, when calculating the period, we must also use the corresponding unit of seconds (s).

For 1 MHz, the period is correctly calculated as 1 microsecond (μs) or 1 x 10^-6 seconds. This is because 1 MHz is equivalent to 1 million cycles per second, and when we take the inverse, we get 1/1,000,000 seconds, which can be expressed as 1 μs.

For 2 MHz, the period is correctly calculated as 0.5 microseconds or 0.5 x 10^-6 seconds. This is because 2 MHz is equivalent to 2 million cycles per second, and when we take the inverse, we get 1/2,000,000 seconds, which can be expressed as 0.5 μs.

In engineering notation, the prefix "micro" (μ) represents 10^-6, while the prefix "nano" (n) represents 10^-9. Therefore, 0.5 μs is equivalent to 500 ns, and both units are correct in this context.

I understand that it may seem more intuitive to use 500 ns instead of 0.5 μs, but it is important to follow the standard units used in engineering notation to avoid confusion and ensure accuracy in calculations. I hope this explanation helps clarify the use of units in this problem.