Units, prefixes and scientific notation

A measurement is always two things: a number and a unit. "Five" means nothing until you say five what. Electronics uses a shared set of units called the SI, the international system of units. Chapter 2 explains what each one measures. For now, learn the names.

• Volt, written V, measures voltage, the electrical "push". A board pin might sit at 3.3 V.
• Amp, written A, measures current, how much electricity flows.
• Ohm measures resistance, how hard a part makes it to flow. Its symbol is \Omega, the Greek capital letter omega. A resistor might be 220 ohms, written 220 \Omega.
• Farad, written F, measures capacitance, how much charge a capacitor can store.
• Hertz, written Hz, counts how many times something repeats each second. A clock running at 48 million ticks a second is 48 million Hz.
• Watt, written W, measures power.
• Second, written s, measures time.

Capital and small letters mean different things, so copy them exactly. A small m and a capital M are a billion times apart, as the next part shows. Put a space between the number and the unit, as in 5 V. Don't add an "s" for more than one: 5 V, never 5 Vs.

Every measurement is a number and a unit, the standard amount it counts in. Two shorthands keep the numbers short: a prefix, a letter in front of the unit that multiplies it by a power of ten, and scientific notation, which writes a number as a value times a power of ten. Both are built in the next part. The units here belong to the SI, the international system of units. Chapter 2 explains what each quantity is; this table is the vocabulary.

\Omega is the Greek capital letter omega, the symbol for the ohm. Unit symbols are case-sensitive: s is a second, S is a different unit; m (milli, below) and M (mega) differ by a factor of a billion. Write a space between the number and the symbol, 5 V, and never add an "s" for plurals: 5 V, not 5 Vs.

A prefix is a short word, or one letter, stuck on the front of a unit to make it bigger or smaller. Each step is a factor of a thousand. Think of a ladder where every rung is a thousand times the one below.

• Mega, written capital M, means a million. 1 megohm is 1 000 000 ohms.
• Kilo, written small k, means a thousand. 4.7 kilohms is 4700 ohms.
• No prefix means just the unit itself.
• Milli, written small m, means a thousandth. 8 milliamps is 0.008 amps.
• Micro means a millionth. Its symbol is \mu, the Greek small letter mu. 100 microfarads is 0.0001 farads. Keyboards rarely have a mu key, so shops often type a small u instead: "100uF".
• Nano, written n, means a billionth.
• Pico, written p, is a thousand times smaller again.

Computer memory also uses giga, capital G, for a billion.

To convert, count rungs. Going up one rung, say from milliamps to amps, divide by 1000. Going down one rung, multiply by 1000. The amount stays the same; only the label changes. So 0.1 microfarads, 100 nanofarads and 100 000 picofarads are all one capacitor. To compare two values, first move them onto the same rung.

You will also see scientific notation. It writes a number as something between 1 and 10, times ten raised to a power. 4700 becomes 4.7 × 10³. The little 3 says "the decimal point moved three places right". 0.008 becomes 8 × 10⁻³, three places left. Engineering notation only uses powers of 3, so each one matches a prefix: 47 × 10³ ohms is 47 kilohms. Calculators and code write the power after an E. So "4.7E3" means 4.7 × 10³, and "8e-3" means 8 × 10⁻³.

A prefix in front of a unit multiplies it by a fixed power of ten. The prefixes used in electronics go in steps of 1000:

• mega, M, \times 10^{6} (a million): 1\ \text{M}\Omega = 1\,000\,000\ \Omega
• kilo, k, \times 10^{3} (a thousand): 4.7\ \text{k}\Omega = 4700\ \Omega
• milli, m, \times 10^{-3} (a thousandth): 8\ \text{mA} = 0.008\ \text{A}
• micro, \mu, \times 10^{-6} (a millionth): 100\ \mu\text{F} = 0.0001\ \text{F}
• nano, n, \times 10^{-9} (a billionth): 100\ \text{nF} = 0.000\,000\,1\ \text{F}
• pico, p, \times 10^{-12}: 22\ \text{pF}

\mu is the Greek small letter mu. Keyboards rarely have it, so datasheets and shops often write u instead: 100uF means 100\ \mu\text{F}. Computer memory also uses giga, G, \times 10^{9}.

Converting. Moving up one rung (milli to plain, plain to kilo) divides the number by 1000; moving down multiplies it by 1000. The quantity never changes, only how it is written: 0.1\ \mu\text{F} = 100\ \text{nF} = 100\,000\ \text{pF}. To compare two values, put them on the same rung first.

Scientific notation writes a number as a value from 1 to under 10 times a power of ten: 4700 = 4.7 \times 10^{3}, and 0.008 = 8 \times 10^{-3}. The power of ten counts how many places the decimal point moved. Engineering notation keeps the power a multiple of 3, so it lines up with a prefix: 47 \times 10^{3}\ \Omega = 47\ \text{k}\Omega. Calculators and code print the power after an E: 4.7E3 is 4.7 \times 10^{3}, and 8e-3 is 8 \times 10^{-3}.

Parts are small. A tiny printed dot for a decimal point can rub off or be misread. So makers use two shorthand tricks.

Trick one: the letter is the decimal point. The prefix letter sits where the decimal point would go. "4k7" means 4.7 kilohms. "2M2" means 2.2 megohms. "1k0" means 1.0 kilohms. For values below one kilohm, resistors use the letter R as the decimal point. "R47" is 0.47 ohms and "4R7" is 4.7 ohms. Capacitors use the same idea: "4n7" is 4.7 nanofarads. You will see this on circuit drawings too.

Trick two: the capacitor code. Small capacitors often show just three digits. They are read in picofarads, the smallest rung. The first two digits are the number. The third digit says how many zeros to add. So "104" means 10 and then four zeros: 100 000 picofarads. Move up the ladder and that is 100 nanofarads, or 0.1 microfarads. "103" is 10 nanofarads. "220" is 22 with no zeros: 22 picofarads. A letter after the code, like "104K", tells you how close to the marked value the part is guaranteed to be. The seller's table says what each letter means.

Many resistors use coloured stripes instead of print. Chapter 4 teaches those. When you can't tell what a part is, measure it with a multimeter. Chapter 2 shows how.

Parts are tiny and a printed decimal point is easy to lose, so two shorthand systems are common.

The letter is the decimal point (the RKM code, from the standard IEC 60062). The prefix letter replaces the decimal point: 4k7 is 4.7\ \text{k}\Omega, 2M2 is 2.2\ \text{M}\Omega, 1k0 is 1.0\ \text{k}\Omega. For resistors, R marks a decimal point with no prefix: R47 is 0.47\ \Omega and 4R7 is 4.7\ \Omega. The same style appears for capacitors: 4n7 is 4.7\ \text{nF}. You will meet it on circuit drawings as well as on parts.

The three-digit capacitor code. Small ceramic capacitors carry three digits, read in picofarads: the first two digits are the value and the third is how many zeros follow. 104 is 10 followed by four zeros, 100\,000\ \text{pF} = 100\ \text{nF} = 0.1\ \mu\text{F}. 103 is 10\ \text{nF}, 220 is 22 followed by no zeros, 22\ \text{pF}. A letter after the code, such as 104K, gives the tolerance (how far the real value may be from the marked one); the part's datasheet or the seller's table says what the letter means.

Through-hole resistors usually carry coloured bands instead of text. Chapter 4 §1 reads them. When a marking is ambiguous, a multimeter settles it (Chapter 2 §5).