Last updated: May 2026
Convert between scientific notation, E notation, engineering notation, and standard form — instantly.
Rules for Scientific Notation Arithmetic
SI Prefixes Reference
| Prefix | Symbol | Power of 10 | Value |
|---|---|---|---|
| Tera | T | 1012 | 1,000,000,000,000 |
| Giga | G | 109 | 1,000,000,000 |
| Mega | M | 106 | 1,000,000 |
| Kilo | k | 103 | 1,000 |
| Milli | m | 10−3 | 0.001 |
| Micro | μ | 10−6 | 0.000001 |
| Nano | n | 10−9 | 0.000000001 |
| Pico | p | 10−12 | 0.000000000001 |
Real-World Examples
| Quantity | Scientific notation | Value / unit |
|---|---|---|
| Speed of light | 3 × 108 m/s | 299,792,458 m/s |
| Mass of a proton | 1.67 × 10−27 kg | 0.00000000000000000000000000167 kg |
| Earth's mass | 5.97 × 1024 kg | 5,970,000,000,000,000,000,000,000 kg |
| Avogadro's number | 6.022 × 1023 | molecules per mole |
| Planck's constant | 6.626 × 10−34 J·s | quantum of action |
| Distance to the Moon | 3.84 × 108 m | 384,400 km |
Scientific notation expresses any number as a × 10n, where 1 ≤ |a| < 10 and n is an integer.
E notation (used in computers and calculators) writes the same number as aEn, e.g. 4.5E-4.
Engineering notation restricts the exponent to multiples of 3, aligning with SI prefixes (milli, micro, nano, kilo, mega, etc.).
Conversion steps: (1) Write the number in the form a × 10n. (2) Adjust a so that 1 ≤ |a| < 10, incrementing or decrementing n accordingly. (3) For engineering notation, round n down to the nearest multiple of 3 and adjust a.
Why do scientists use scientific notation instead of writing out the full number?
Three reasons: readability, precision, and avoiding errors. Writing 6.022 × 10²³ is far more readable than 602,200,000,000,000,000,000,000. It also makes the number of significant figures immediately clear — 6.022 × 10²³ has four significant figures; the full number obscures that. And it dramatically reduces transcription errors when working with very large or very small numbers.
What does a negative exponent mean in scientific notation?
A negative exponent means the number is very small — a fraction, not a large number. 10⁻³ = 0.001 (one thousandth). 10⁻⁹ = 0.000000001 (one billionth). So 1.67 × 10⁻²⁷ kg (the mass of a proton) is an extremely small number: 0.00000000000000000000000000167 kg. The negative exponent tells you how many places to move the decimal point to the left.
What is the difference between scientific notation and E notation?
They represent the same thing with different symbols. Scientific notation uses × 10ⁿ: 4.5 × 10⁻⁴. E notation (used on calculators and in programming) writes this as 4.5E-4 or 4.5e-4. The "E" stands for "exponent" and means "× 10 to the power of." You'll see E notation on calculator displays and in code (Python, JavaScript, C, etc.) because it's easier to type than a superscript.
How do you add and subtract numbers in scientific notation?
You must match exponents first. Example: (3 × 10⁴) + (2 × 10³). Convert the second term: 2 × 10³ = 0.2 × 10⁴. Now add: (3 + 0.2) × 10⁴ = 3.2 × 10⁴. Multiplication and division are easier — multiply or divide the coefficients and add or subtract the exponents: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷.
What is engineering notation and how does it differ from scientific notation?
Engineering notation restricts the exponent to multiples of 3 (0, 3, 6, 9, −3, −6, etc.), which aligns with SI prefixes. So instead of 4.7 × 10⁴, engineering notation writes 47 × 10³ (= 47 kilo, or 47k). This makes it easier to read values in the context of real-world measurements. 0.000047 amps in engineering notation is 47 × 10⁻⁶ A = 47 μA (microamps) — a unit you can actually say out loud.