Scientific Notation Calculator
Convert any number to and from scientific notation, round to significant figures, and perform arithmetic in scientific notation.
Scientific notation reference
| Standard | Scientific | Engineering |
|---|---|---|
| 0.000001 | 1 × 10⁻⁶ | 1 × 10⁻⁶ |
| 0.001 | 1 × 10⁻³ | 1 × 10⁻³ |
| 1,000 | 1 × 10³ | 1 × 10³ |
| 1,000,000 | 1 × 10⁶ | 1 × 10⁶ |
| 6,674,000,000 | 6.674 × 10⁹ | 6.674 × 10⁹ |
| Speed of light (~3×10⁸ m/s) | 3 × 10⁸ | 300 × 10⁶ |
Why scientific notation exists
Physics and chemistry routinely deal with numbers like 0.000 000 000 000 000 000 000 001 673 kilograms (the mass of a proton) or 299 792 458 metres per second (the speed of light). Writing them in full is error-prone and takes up a ridiculous amount of space.
Scientific notation solves this by splitting every number into a coefficient between 1 and 10 and an exponent of 10. The proton mass becomes 1.673 × 10⁻²⁷ kg. The speed of light becomes roughly 3 × 10⁸ m/s. Same numbers, fraction of the space, easier to compare across many orders of magnitude.
How to convert a number to scientific notation
- Move the decimal point until only one non-zero digit is to its left. Count how many places you moved it.
- Write the new number, followed by "× 10n". n is positive if you moved the decimal left, negative if you moved it right.
Example: 47,300 → move the decimal 4 places left → 4.73 → written as 4.73 × 10⁴. Example the other way: 0.0000082 → move the decimal 6 places right → 8.2 → written as 8.2 × 10⁻⁶.
Scientific notation vs engineering notation vs E-notation
These three look similar but follow different rules:
- Scientific notation: coefficient always between 1 and 10 (like 4.73 × 10⁴).
- Engineering notation: exponent is always a multiple of 3, matching SI unit prefixes (nano-, micro-, milli-, kilo-, mega-, giga-). 47,300 becomes 47.3 × 10³, or 47.3 kilo-.
- E-notation: the calculator/computer form. 4.73 × 10⁴ is written 4.73E4 or 4.73e4. Widely used on scientific calculators, in programming languages and spreadsheets.
This tool converts between all three. Pick whichever fits your context: scientific for physics papers, engineering for electronics, E-notation for code and spreadsheets.
Arithmetic with scientific notation
Multiplying and dividing scientific-notation numbers is easy: multiply (or divide) the coefficients, then add (or subtract) the exponents.
(2 × 10³) × (4 × 10⁵) = 8 × 10⁸. (6 × 10⁷) ÷ (3 × 10²) = 2 × 10⁵.
Adding and subtracting is harder because the exponents must match first. To add 3 × 10⁴ and 4 × 10³, rewrite the smaller one as 0.4 × 10⁴ and add coefficients: (3 + 0.4) × 10⁴ = 3.4 × 10⁴.
Common orders of magnitude to remember
| Value | Scientific | Everyday reference |
|---|---|---|
| 10⁰ | 1 | Unit |
| 10³ | Thousand | kilogram |
| 10⁶ | Million | megabyte |
| 10⁹ | Billion | gigabyte / a person's approximate second-count in 30 years |
| 10¹² | Trillion | terabyte / UK national debt scale |
| 10⁻³ | Milli- | millimetre, millisecond |
| 10⁻⁶ | Micro- | bacteria size, microsecond |
| 10⁻⁹ | Nano- | transistor gate, DNA base pair spacing |
Frequently asked questions
What is the difference between scientific notation and standard form?
They are the same thing. UK schools call it "standard form"; US schools tend to say "scientific notation". Coefficient between 1 and 10, followed by a power of 10.
Can I enter negative numbers?
Yes. −4.73 × 10⁴ works. The minus sign belongs on the coefficient; the exponent tells you the order of magnitude and does not need to be signed for the number itself to be negative.
Why does my calculator show 6.02E23 instead of 6.02 × 10²³?
Calculators use E-notation as a compact print form for the same number. 6.02E23 and 6.02 × 10²³ are identical (both represent Avogadro's constant). It is easier to type an "E" than a superscript.
How many significant figures should I keep in the coefficient?
As many as the source measurement gives you. Multiplying two values does not add precision — the answer has as many significant figures as the least-precise input.
Is 0.5 × 10⁴ valid scientific notation?
No — the coefficient must be at least 1 and less than 10. Rewrite it as 5 × 10³. This calculator will normalise for you.