Engineering Notation — Definition, Formula & Examples

Engineering notation is a way of writing very large or very small numbers so that the exponent on the power of 10 is always a multiple of 3 (such as 3, 6, 9, −3, −6). The coefficient is adjusted to fall between 1 and 999.

A number in engineering notation has the form $a \times 10^n$ , where $1 \le |a| < 1000$ and $n$ is an integer divisible by 3. This convention aligns exponents with the metric prefixes kilo ( $10^3$ ), mega ( $10^6$ ), milli ( $10^{-3}$ ), micro ( $10^{-6}$ ), and so on.

Key Formula

a \times 10^{n}, \quad 1 \le |a| < 1000, \quad n \in \{\ldots, -6, -3, 0, 3, 6, \ldots\}

Where:

$a$ = The coefficient, a number with absolute value from 1 up to (but not including) 1000
$n$ = The exponent, which must be a multiple of 3

How It Works

Start by writing the number in standard scientific notation. Then shift the decimal point left or right (in steps of one place) until the exponent becomes a multiple of 3, adjusting the coefficient accordingly. For every place you move the decimal to the right, decrease the exponent by 1; for every place to the left, increase it by 1. The final coefficient must satisfy

1 \le |a| < 1000

Worked Example

Problem: Express 47,200,000 in engineering notation.

Step 1: Write the number in scientific notation.

47{,}200{,}000 = 4.72 \times 10^{7}

Step 2: The exponent 7 is not a multiple of 3. The nearest lower multiple of 3 is 6. Move the decimal one place to the right to compensate for reducing the exponent by 1.

4.72 \times 10^{7} = 47.2 \times 10^{6}

Step 3: Check: the coefficient 47.2 is between 1 and 1000, and the exponent 6 is a multiple of 3.

47.2 \times 10^{6}

Answer:

47.2 \times 10^{6}

(equivalent to 47.2 mega-units in metric prefix form)

Why It Matters

Engineering notation is the standard way electrical engineers, physicists, and technicians express quantities like 4.7 kΩ (

4.7 \times 10^{3}

ohms) or 220 nF (

220 \times 10^{-9}

farads). Because each exponent maps directly to a metric prefix, converting between the notation and real-world unit labels is immediate—no extra mental arithmetic required.

Common Mistakes

Mistake: Using any convenient exponent instead of restricting it to a multiple of 3 (e.g., writing

4.72 \times 10^{7}

and calling it engineering notation).

Correction: Always adjust the coefficient so the exponent lands on …, −6, −3, 0, 3, 6, 9, … . The coefficient can be larger than 10, up to 999.