About Scientific Notation
Scientific notation (also called standard form or exponential notation) is a way of writing very large or very small numbers compactly. It expresses a number as the product of two parts: a mantissa — a decimal number between 1 and 10 — and a power of 10. So 299,792,458 becomes 2.99792458 × 10⁸, and 0.0000000000000000001602 becomes 1.602 × 10⁻¹⁹.
This notation is universal in science, engineering and computing because it makes orders of magnitude instantly visible: you can tell at a glance whether a value is in the thousands, millions or billions. It also removes ambiguity about significant figures — the number of digits in the mantissa tells you exactly how precisely the value is known.
The four formats
| Format | Example | Notes |
|---|---|---|
| Decimal | 1234.5 | Everyday form with explicit digits |
| Scientific | 1.2345 × 10³ | One digit before the decimal point |
| Engineering | 1.2345e3 | Exponent is always a multiple of 3 |
| E-notation | 1.2345e+3 | Programming / calculator form |
How scientific notation works
Take any number and slide the decimal point left or right until there is exactly one non-zero digit to its left. The number of positions you moved is the exponent. Moving left makes a positive exponent; moving right makes a negative exponent. For 1234.5: slide the decimal 3 places left → 1.2345 × 10³. For 0.00042: slide the decimal 4 places right → 4.2 × 10⁻⁴.
Scientific vs engineering notation
| Value | Scientific | Engineering | SI prefix |
|---|---|---|---|
| 1,500 | 1.5 × 10³ | 1.5 × 10³ | kilo (k) |
| 15,000 | 1.5 × 10⁴ | 15 × 10³ | — |
| 0.0025 | 2.5 × 10⁻³ | 2.5 × 10⁻³ | milli (m) |
| 0.00025 | 2.5 × 10⁻⁴ | 250 × 10⁻⁶ | — |
| 4,700,000 | 4.7 × 10⁶ | 4.7 × 10⁶ | mega (M) |
Both use the same underlying value. Engineering notation is preferred by engineers because the exponent maps directly to an SI prefix — every 3-step change in exponent corresponds to a new prefix (k, M, G, m, µ, n…). Scientific notation is more common in physics and general science because it uses exactly one mantissa digit.
SI prefixes at a glance
| Prefix | Symbol | Power of 10 |
|---|---|---|
| Tera | T | 10¹² |
| Giga | G | 10⁹ |
| Mega | M | 10⁶ |
| Kilo | k | 10³ |
| Milli | m | 10⁻³ |
| Micro | µ | 10⁻⁶ |
| Nano | n | 10⁻⁹ |
| Pico | p | 10⁻¹² |
Famous numbers in scientific notation
| Quantity | Value | Scientific |
|---|---|---|
| Speed of light | 299,792,458 m/s | 2.998 × 10⁸ m/s |
| Avogadro's number | 602,214,076,000,000,000,000,000 | 6.022 × 10²³ |
| Electron charge | 0.0000000000000000001602 C | 1.602 × 10⁻¹⁹ C |
| Planck constant | 0.0000000000000000000000000000000006626 J·s | 6.626 × 10⁻³⁴ J·s |
| Diameter of proton | 0.0000000000000017 m | 1.7 × 10⁻¹⁵ m |
| Distance to Sun | 149,600,000,000 m | 1.496 × 10¹¹ m |
Common use cases
Science & Physics
Express huge or tiny values like Planck constant or Avogadro's number.
Engineering
Match exponents to SI prefixes for readability.
Calculator Input
Convert to E-notation for programming languages and calculators.
Education
Teach or learn how exponents and mantissas work.
Astronomy
Express distances, masses and luminosities across astronomical scales.
Chemistry
Work with atomic masses, concentrations and quantum values.
Privacy and accuracy
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