What scientific notation is
Scientific notation (called standard form in the UK) writes a number as a value between 1 and 10 multiplied by a power of ten:
number = a × 10n, where 1 ≤ |a| < 10 and n is a whole number
The part a is called the coefficient (or significand) and n the exponent. Very large and very small numbers become short and easy to compare: the speed of light, 299,792,458 m/s, is 2.99792458 × 108 m/s, and the charge of an electron, 0.000 000 000 000 000 000 160 2 coulombs, is 1.602 × 10−19 C.
How to convert, step by step
- Move the decimal point until exactly one non-zero digit is to its left.
- Count how many places you moved it. That count is the exponent.
- If you moved the point to the left (a big number), the exponent is positive; if you moved it to the right (a small number), it is negative.
| Number | Scientific notation | E notation | Engineering |
|---|---|---|---|
| 299,792,458 | 2.99792458 × 108 | 2.99792458E+8 | 299.792458 × 106 (M) |
| 123,456 | 1.23456 × 105 | 1.23456E+5 | 123.456 × 103 (k) |
| 0.0072 | 7.2 × 10−3 | 7.2E−3 | 7.2 × 10−3 (m) |
| 0.000045 | 4.5 × 10−5 | 4.5E−5 | 45 × 10−6 (µ) |
To go back, do the reverse: a positive exponent moves the decimal point that many places to the right, a negative one moves it to the left, filling gaps with zeros. 6.02 × 1023 becomes 602,000,000,000,000,000,000,000. Type either form into the calculator and it shows the other.
E notation on calculators and spreadsheets
Calculators, Excel, Google Sheets and programming languages write the "× 10 to the power" part as the letter E: 6.02E23 or 6.02e+23 means 6.02 × 1023, and 1.6E−19 means 1.6 × 10−19. It is not the mathematical constant e (2.718…). You can type E notation directly into the box above.
Engineering notation and SI prefixes
Engineering notation is a variant where the exponent is always a multiple of 3, so the coefficient is between 1 and 1,000. The advantage is that each exponent matches an SI prefix, which is how engineers and electronics datasheets write values:
| Power | Prefix | Example |
|---|---|---|
| 109 | giga (G) | 2.4 × 109 Hz = 2.4 GHz |
| 106 | mega (M) | 15 × 106 W = 15 MW |
| 103 | kilo (k) | 4.7 × 103 Ω = 4.7 kΩ |
| 10−3 | milli (m) | 250 × 10−3 A = 250 mA |
| 10−6 | micro (µ) | 45 × 10−6 m = 45 µm |
| 10−9 | nano (n) | 100 × 10−9 F = 100 nF |
Significant figures
Significant figures are the digits that carry real information. Scientific notation makes them obvious, because every digit in the coefficient is significant. Rounding the speed of light to 3 significant figures gives 3.00 × 108 m/s; the trailing zeros show the value is known to three figures, which you cannot tell from writing "300,000,000". Choose a number of significant figures in the calculator to round the result; leave it on "keep all digits" to see the exact value you entered.
Multiplying and dividing in scientific notation
Multiply the coefficients and add the exponents; divide the coefficients and subtract the exponents, then adjust so the coefficient is back between 1 and 10:
- (3 × 108) × (2 × 10−3) = 6 × 105
- (6 × 105) × (5 × 102) = 30 × 107 = 3 × 108
- (8 × 106) ÷ (4 × 102) = 2 × 104
Adding and subtracting needs the same exponent first: 3 × 104 + 5 × 103 = 30 × 103 + 5 × 103 = 35 × 103 = 3.5 × 104.
Common mistakes
- Coefficient out of range. 45 × 10−6 is valid engineering notation but not scientific notation; the scientific form is 4.5 × 10−5.
- Wrong sign on the exponent. Small numbers (less than 1) always have a negative exponent.
- Writing 10E5 for 105. 10E5 means 10 × 105 = 106. One hundred thousand is 1E5.
- Losing precision in spreadsheets. Long ID numbers (card numbers, barcodes) typed into Excel are shown in E notation and only the first 15 digits are kept. Format such cells as text.
Frequently asked questions
How do I write 0.000045 in scientific notation?
Move the decimal point 5 places to the right to get 4.5, so 0.000045 = 4.5 × 10⁻⁵ (4.5E-5).
What does E mean in a number like 6.02E23?
E means 'times ten to the power of'. 6.02E23 is 6.02 × 10²³.
What is the difference between scientific and engineering notation?
Scientific notation keeps the coefficient between 1 and 10; engineering notation uses exponents that are multiples of 3, so the coefficient is between 1 and 1,000 and matches SI prefixes like kilo, mega and micro.
How do I write the speed of light in scientific notation?
299,792,458 m/s = 2.99792458 × 10⁸ m/s, or about 3.00 × 10⁸ m/s to three significant figures.
Sources
- BIPM. The International System of Units (SI Brochure), 9th edition, 2019: SI prefixes and defining constants.
- NIST Special Publication 811, Guide for the Use of the International System of Units, 2008.
Last reviewed 14 October 2026. Results are estimates; see our disclaimer.