What is scientific notation?
Scientific notation is a compact way of writing very large or very small numbers as a coefficient multiplied by a power of ten. A number is in normalised scientific notation when it is written as a × 10ⁿ, where the coefficient a is at least 1 but less than 10, and the exponent n is a whole number. The mass of the Earth, 5,972,000,000,000,000,000,000,000 kg, becomes 5.972 × 10²⁴ kg — the same value, but readable at a glance. Scientific notation is also called standard form in British and Norwegian schools, and it is the notation physics, chemistry and astronomy rely on daily.
How do you convert a number to scientific notation?
Move the decimal point until exactly one non-zero digit sits to its left, then count how many places you moved it. If you moved the point to the left, the exponent is positive; if you moved it to the right, the exponent is negative. Take 10,550,000: shifting the decimal point seven places left gives the coefficient 1.055, so the result is 1.055 × 10⁷. For 0.00052, shifting four places right gives 5.2, so the result is 5.2 × 10⁻⁴. This calculator accepts input in any of these forms — a plain decimal, 5.2e-4, or 5.2 x 10^-4 — and returns every other form at once.
What is the scientific notation formula?
The formula is a × 10ⁿ with 1 ≤ |a| < 10 and n an integer. The exponent n is the order of magnitude of the number: it tells you roughly how big the value is without reading a single digit of the coefficient. A number with exponent 6 is a million-ish; a number with exponent −9 is a billionth-ish. To recover the original number, multiply the coefficient by ten raised to that exponent, which is the same as shifting the decimal point n places. Rounding a coefficient sensibly is a separate question — our significant figures calculator handles that side of the work.
What are some scientific notation examples?
A few worked conversions in both directions:
- 300 = 3 × 10² — the decimal point moves two places left.
- 4321.768 = 4.321768 × 10³ — three places left, all digits kept.
- 0.2 = 2 × 10⁻¹ — one place right, so the exponent is negative.
- 6,720,000,000 = 6.72 × 10⁹ — nine places left.
- 1.2 × 10⁻⁵ = 0.000012 — converting back, the point moves five places right.
When is scientific notation useful?
It is useful whenever a number has more zeros than meaningful digits. Chemistry uses it for Avogadro's number, 6.022 × 10²³ particles per mole; physics uses it for the speed of light, 2.998 × 10⁸ m/s; biology uses it for cell diameters around 1 × 10⁻⁵ m. It also makes numbers comparable: 3 × 10⁸ is obviously a thousand times larger than 3 × 10⁵, a comparison that is much slower to make from 300000000 and 300000. Calculators and spreadsheets switch to this notation automatically once a value exceeds their display width, which is why you see 1.2E+25 on a screen. For summarising sets of such measurements, our mean, median and mode calculator works on the same numbers.
What is the difference between scientific notation, E notation, and engineering notation?
All three express the same value; only the presentation differs. Scientific notation writes the power of ten explicitly, as in 1.055 × 10⁷. E notation replaces "× 10" with the letter e, giving 1.055e7 — this exists because keyboards, programming languages and calculator displays cannot easily show a superscript. Engineering notation restricts the exponent to multiples of three so it lines up with SI prefixes, so 1.055 × 10⁷ becomes 10.55 × 10⁶, read as 10.55 mega-. In engineering notation the coefficient may sit anywhere between 1 and 1000, which is the one rule that separates it from strict scientific notation. This calculator shows all three side by side.
How do you convert scientific notation back to standard form?
Read the exponent and move the decimal point that many places — right for a positive exponent, left for a negative one — padding with zeros as needed. For 1.055 × 10⁷, move the point seven places right and pad: 10,550,000. For 5.2 × 10⁻⁴, move it four places left and pad with leading zeros: 0.00052. The trap is trusting a spreadsheet or programming language to do this for you, because most switch back to exponential display above 10²¹ and lose the plain digits. Entering the value here returns the fully written-out decimal form no matter how large the exponent. If you are working with percentages of such values, our percentage calculator is the next stop.