Converting Quantities to Values with Metric Prefixes

After making calculations with the decimal values, for example, you may need to convert back to metric prefixes. Let's look at how that works.

Step 1: Decide how many places to the left or right to shift the decimal point and select the corresponding metric prefix.  For example, if you shift it left by 3, that’ll be k (kilo), or if you shift it left by 3 more (for a total of 6), that’ll be M (mega).  For shifting to the right, 3 would be m (milli), 6 would be µ (micro), and so on…  Tip: Make sure to use multiples of 3.

Step 2: Find the decimal value for the metric prefix in the SI Metric Prefixes table and make a fraction of metric prefix / decimal value.

Step 3: Multiply your quantity by the fraction.

Step 4: Calculate the result.

Example: Convert 38,000 Hz so that it has a metric prefix.  Hint: In engineering notation, it’s usually preferable for the integer part of the quantity to be in the 1...999 range.  

Here are examples of how metric prefixes change the schematics you’ve been working with.  Again, shoot for an integer portion in the 1...999 range.

Remember from earlier, how if you multiply some quantity by 1, the result is that same quantity?  The example started with 1000 = k and divided both sides of the equal sign by k for a result of 1 = 1000 / k.  You could divide both sides by 1000 instead for 1 = k / 1000.  Then, starting with 2000 Ω, you can multiply by k / 1000.  The thousands cancel, and the result is 2 kΩ.  

(View full size: muam-multiply-by-one-val-to-prefix.mp4)