SI Prefixes

## SI prefixes

Note: when expressing decimal fractions, commas are not used to the right of the decimal point. For example, "0.0000123" is the correct way to express 12.3 1-millionths of something. Here we will use "0.000,012,3" to help visualize the decimal places and the prefixes to use.

Working in electronics often requires working with very large and very small numbers, such as thousands of ohms or millionths of farads. To simplify writing these numbers, SI prefixes (International System of Units) are used to represent multipliers. For example, 1,000 ohms is expressed as 1 kiloohm, 1k ohm, or just 1k. A capacitance of 0.000,001 farad is expressed as 1 microfarad, 1μF or just 1μ.

 SI Prefixes Commonly Used in Electronics Name Symbol Multiplier Scientific Notation Tera T X 1,000,000,000,000 1.00x1012 giga G x 1,000,000,000 1.00x109 mega M x 1,000,000 1.00x106 kilo k x 1,000 1.00x103 milli m x 0.001 1.00x10-3 micro μ x 0.000,001 1.00x10-6 nano n x 0.000,000,001 1.00x10-9 pico p x 0.000,000,000,001 1.00x10-12

The prefixes hecto (x100),  deca (x10), deci (x0.1) and centi (x0.01) are not normally used for electronic units. You may use centimeters to measure distance by you are unlikely to hear of a centivolt.

#### Examples:

In the chart below, each row shows different representations of the same value. The last column uses engineering notation.

 4,700 ohms 4.7 kiloohms 4.7 kΩ 4.70x103 ohms 0.01 henry 10 millihenrys 10 mH 10.0x10-3 henrys 0.0001 farad 100 microfarads 100 μF 100x10-6 farads

### Using prefixes

Large numbers are fairly simple to add prefixes to. If the quantity is in the thousands, the prefix is kilo. For example, 1,000 volts is 1 kilovolt, 10,000 volts is 10 kilovolts, 2,500 volts is 2.5 kilovolts. If a quantity is in the millions, the prefix is mega. For example, 470 million ohms is 470 megaohms. This works the same for billions, for which the prefix is giga (pronounced with a hard 'G' or a soft 'G,' either is correct) and trillions, for which the prefix is tera. Here are some more examples:

 1,250 volts = 1.25 kilovolts (1.25 kV) 33,000 ohms = 33 kiloohms (33 kΩ) 1,360,000 hertz = 1.36 megahertz (1.26 MHz) 25,000,000,000 hertz = 25 gigahertz (25 GHz)

Another way to look at it is: for thousands, move the decimal point three places to the left to convert to kilo. For millions, move the decimal point six places to the left to convert to mega, nine places for giga and 12 places for tera.

 Move DP three places to the left

### Mixing prefixes

Sometimes numbers will be specified with the "wrong" prefix. This is usually done simply to keep a list of values in the same prefix. For example, 500,000 hertz should be 500 kilohertz. However, if this quantity falls in a list where the other values are specified in megahertz, it may be expressed as 0.5 megahertz. For example, look at the following table of frequencies.

 3.5  2.7 700 1.6 MHz MHz kHz MHz

At a glance, you might see the 700 kHz and think it is 700 MHz. Now, look at the following list of the same values.

 3.5 2.7 0.7 1.6 MHz MHz MHz MHz

Here the 700 kHz is it is expressed in MHz to be consistent with the other frequencies. It is unlikely that this would be mistaken for anything other than what it is. Another example is seen on the AM radio dial. AM radio frequencies are usually expressed in kilohertz, even though more than half of the allotted band is above 1 MHz. For example, KSL, in Salt Lake City, broadcasts on a frequency of 1.16 MHz (1,160,000 Hz). However, this is usually expressed as 1,160 kHz (1160 on the AM dial). Both express the same frequency.

Small numbers may be a bit harder to follow because you may not be used to working with thousandths and millionths, etc. Thousandths of amperes are expressed as milliamperes. For example, 0.001 ampere is 1 milliampere (1.mA), 0.01 ampere is 10 milliamperes (10.mA), 0.0025 ampere is 2.5 milliamperes (2.5.mA). Millionths of farads are expressed as microfarads. For example, 0.000,001 farad is 1 microfarad (1.μF). Here are some more examples:

 0.25 volt = 250 millivolts (250 mV) 0.000,022 farad = 22 microfarads (22 μF) 0.016,7 watt = 16.7 milliwatts (16.7 mW) 0.000,000,000,33 farad = 330 picofarads (330 pF)

To convert thousandths to milli, move the decimal point three places to the right. To convert millionths to micro, move the decimal point six places to the right. Nine places to the right converts to nano and 12 places converts to pico.

 Move DP three places to the right

Some people can use the following visualizations, but they don't work for everyone.

 For example:    0.245 A = 245 mA    0.033 A = 33 mA    0.007 A = 7 mA 0.005,2 A = 5.2 mA For example:    0.000,300 A = 300 μA    0.000,025 A = 25 μA    0.000,004 A = 4 μA 0.000,007,5 A = 7.5 μA

As with large numbers, some values will be specified with the "wrong" prefix. The most common example is millifarads and nanofarads. Milli and nano are rarely used to specify farads (at least in the U.S.). Instead, 0.001 farad would be 1,000 microfarads, 0.000,000,010 farad would be 10,000 picofarads. Look at the following list of capacitances:

 470 2.7 1,500 0.47 μF μF μF μF

You might think of 1,500 μF as 1.5 millifarads (1.5 mF), but that is rarely used in labeling capacitors (see confusion alert below). Likewise, you might be tempted to express 0.47 μF as 470 nanofarads (470 nF), but that is also rarely used in labeling capacitors.

Many capacitors may be labeled with “mF” (lower case “m”). In this case, "mF" means microfarads, not millifarads. This is supposedly because the labeling equipment owned by the manufacturers is not capable of printing the Greek letter mu (μ).2 Capacitors are also commonly labeled with “MF” (upper case “M”). These are not megafarads. They are still microfarads.

Also, even though it is entirely proper and most common to express something like 0.001 watt as 1 milliwatt (1 mW), you might find it expressed as 1,000 microwatts (1,000 μW). They are both the same quantity. It just depends on the context and who is expressing it. Here are some examples.

 0.002 A = 2 mA = 2,000 μA 0.002,45 W = 2.45 mW = 2,450 μW 0.000,35 A = 350 μA = 0.35 mA 0.000,000,003,3 F = 0.003,3 μF = 2,500 pF

Some people are helped by the following visualization (based on the visualizations above).

This illustrates that each range has a 1's column, a 10's column and a 100's column (remember your 5th-grade arithmetic). It also shows that the 1's column of the milli group is also the 1,000's column of the micro group. Think of 0.002 amps as two times 1,000 microamps or 2,000 microamps.

Exercise:

M
ake the following conversions. Be sure to convert to the specified units. For example, 0.012 amperes would most likely be specified as 12 mA. However, if the problem asks for μA, specify the answer as 12,000 μA.1

 0.022 A = ______ mA 0.000,23 F = ______ μF 33,000 ______ kΩ 250,000 Hz = ______ kHz 250,000 Hz = ______ MHz 0.2 A = ______ mA 0.003 W = ______ mW 0.003 W = ______ μW 0.000,23 V = ______ mV 470 kΩ = __________ Ω 2.7 μA = __________ A 500 mA = ________ A

The term "pico" for one trillionth is fairly new. Up to the mid 1960s, the term micro-micro (1 millionth of 1 millionth) was used instead. Therefore, in older documents, you might find the term micro-microfarad ( μμF) used for trillionths of farads instead of picofarads (pF).

### Formal usage

In formal documentation, observe proper capitalization (see the tables above). Note that the SI symbols for Tera, Giga and Mega use upper case where the rest of the SI prefixes use all lower-case. In formal documentation, “amps” should never be used in place of “A” or “amperes.”

SI Prefixes

 1 Answers to exercise:

 22 mA   | 250 kHz   | 3 mW   | 470,000 Ω   | 230 μF   | 0.25 MHz   | 3,000 μW   | .000,002,7 A   | 33 kΩ   200 mA   0.23 mV   0.5 A

 2 Pronounced something like “myew” (one syllable).