Case 1
- Number
- 47000
47 × 10³ (k)
Open with these valuesEngineering Notation Converter
47 × 10³ (k)
Result: 47 × 10³ (k)Engineering notation writes a number with a coefficient between 1 and 1000 and an exponent that is always a multiple of three, so it lines up directly with SI prefixes. 47000 becomes 47 × 10³, which is 47 k; 0.0042 becomes 4.2 × 10⁻³, which is 4.2 m.
The numbers at a glance
| Number | Result |
|---|---|
| 0.0000000000 | 0.000000 |
| 20,000.0000000000 | 20.000000 |
| 40,000.0000000000 | 40.000000 |
| 47,000.0000000000Your value | 47.000000 |
| 60,000.0000000000 | 60.000000 |
| 80,000.0000000000 | 80.000000 |
Worked examples
Case 2
- Number
- 0.0042
4.2 × 10⁻³ (m)
Open with these valuesCase 3
- Number
- 5e-7
500 × 10⁻⁹ (n)
Open with these valuesHow it's calculated
value = coefficient × 10^exponent, exponent a multiple of 3
- StepEnter the decimal number you want to rewrite — 47000 or 0.0042.
- StepMove the decimal point in steps of three until the coefficient is 1 to 1000.
- ResultRead the exponent and its SI prefix: 10³ is kilo, 10⁻³ is milli.
What this number means
Engineering notation writes a number as a coefficient times a power of ten, with one extra rule: the exponent must be a multiple of three. That single rule is the whole difference from scientific notation, and it is what makes the result readable as a unit. Scientific notation turns 47000 into 4.7 × 10⁴, and there is no prefix for 10⁴. Engineering notation turns it into 47 × 10³, and 10³ is kilo — so a 47000 Ω resistor is simply 47 kΩ. Because the exponent moves in steps of three, the coefficient needs room: its absolute value runs from 1 up to 1000, not up to 10. To convert by hand, shift the decimal point three places at a time until the coefficient lands in that range, and count the shifts in threes for the exponent. The prefixes go up as kilo (10³), mega (10⁶) and giga (10⁹), and down as milli (10⁻³), micro (10⁻⁶) and nano (10⁻⁹). Engineers use this because it keeps numbers in the units people actually say out loud: a 1500000 Hz signal is awkward, 1.5 MHz is not. Zero is the one special case — it has no leading digit to anchor an exponent, so it is reported as 0 × 10⁰.
The exponent is always a multiple of three
That is the only difference from scientific notation, and it is why every result maps onto an SI prefix. The coefficient gets the extra room: from 1 up to 1000.
SI prefixes
Kilo (10³), mega (10⁶) and giga (10⁹) for large values; milli (10⁻³), micro (10⁻⁶) and nano (10⁻⁹) for small ones. So 2.2 × 10⁻⁶ F reads as 2.2 µF.
Zero has no exponent
Zero is reported as 0 × 10⁰, since it has no leading digit to anchor an exponent. Every other number returns a coefficient with an absolute value between 1 and 1000.
Commonly misread
Engineering notation keeps the coefficient between 1 and 10.
That is scientific notation. Here the exponent is fixed to multiples of three, so the coefficient runs from 1 up to 1000.
12345.6 is 1.23456 × 10⁴ in engineering notation.
10⁴ is not a multiple of three. The engineering form is 12.3456 × 10³, that is 12.3456 k.
0.0000005 has to be written as 0.5 × 10⁻⁶.
The coefficient must be at least 1, so the exponent drops another step: 500 × 10⁻⁹, that is 500 n.
Reference table
| Number | Engineering notation | SI prefix |
|---|---|---|
| 0.0000005 | 500 × 10⁻⁹ | n (nano) |
| 0.0042 | 4.2 × 10⁻³ | m (milli) |
| 7 | 7 × 10⁰ | — (none) |
| 2200 | 2.2 × 10³ | k (kilo) |
| 12345.6 | 12.3456 × 10³ | k (kilo) |
| 47000 | 47 × 10³ | k (kilo) |
| 1000000 | 1 × 10⁶ | M (mega) |
| 1500000 | 1.5 × 10⁶ | M (mega) |
Questions
How do I convert a number to engineering notation?
Move the decimal point in steps of three places until the coefficient lands between 1 and 1000, and let the number of places set the exponent, which is then a multiple of three. For example, 47000 becomes 47 × 10³ and 0.0042 becomes 4.2 × 10⁻³.
How is engineering notation different from scientific notation?
Scientific notation keeps the coefficient between 1 and 10 and allows any exponent, so 47000 is 4.7 × 10⁴. Engineering notation forces the exponent to a multiple of three and lets the coefficient run up to 1000, so 47000 is 47 × 10³ — which lines up with the SI prefix kilo.
What are SI prefixes?
SI prefixes are names for powers of ten that are multiples of three: kilo (10³), mega (10⁶) and giga (10⁹) for large values; milli (10⁻³), micro (10⁻⁶) and nano (10⁻⁹) for small ones. Engineering notation maps onto them directly, so 2.2 × 10⁻⁶ F reads as 2.2 µF.
Why do engineers use engineering notation?
It keeps numbers in the units people actually say out loud. A 1500000 Hz signal is awkward, but 1.5 × 10⁶ Hz is simply 1.5 MHz. Because the exponent always sits on a prefix boundary, the value translates straight into the kilo-, mega-, milli- or micro-units used on datasheets.
What does the converter do with zero?
Zero is reported as 0 × 10⁰, since it has no leading digit to anchor an exponent. Every non-zero number, positive or negative, returns a coefficient with an absolute value between 1 and 1000 and an exponent that is a multiple of three.
Sources and last check
Information, not professional advice.