Scientific Notation Calculator
Standard form ⇄ a × 10ⁿ, E notation and SI prefixes — plus + − × ÷ with the steps.
In every notation
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- Scientific notation
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- E notation
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- Engineering notation
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- With an SI prefix
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- Decimal (written out)
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How it works
All SI prefixes (quecto to quetta)
| Prefix | Symbol | Factor |
|---|---|---|
| quetta | Q | 10³⁰ |
| ronna | R | 10²⁷ |
| yotta | Y | 10²⁴ |
| zetta | Z | 10²¹ |
| exa | E | 10¹⁸ |
| peta | P | 10¹⁵ |
| tera | T | 10¹² |
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| hecto | h | 10² |
| deca | da | 10¹ |
| deci | d | 10⁻¹ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
| pico | p | 10⁻¹² |
| femto | f | 10⁻¹⁵ |
| atto | a | 10⁻¹⁸ |
| zepto | z | 10⁻²¹ |
| yocto | y | 10⁻²⁴ |
| ronto | r | 10⁻²⁷ |
| quecto | q | 10⁻³⁰ |
BIPM SI Brochure (9th edition); ronna, quetta, ronto and quecto were added in 2022. Engineering notation uses only the powers that are multiples of 3, so hecto, deca, deci and centi do not appear in it.
Answer
This is the last answer worked out. Fix the input above to update it.
- Scientific notation
- —
- E notation
- —
- Engineering notation
- —
- With an SI prefix
- —
- Decimal (written out)
- —
Steps
About the Scientific Notation Calculator
Type a number in any form — 0.00045, 299792458, 6.022e23, 4.5 × 10^-4, or with an SI prefix such as 4.7 k — and see it in scientific notation (a × 10ⁿ with 1 ≤ |a| < 10), in E notation as calculators and spreadsheets show it, in engineering notation (a power of ten that is a multiple of 3) with the matching SI prefix from quecto (10⁻³⁰) to quetta (10³⁰), and written out in full. Each conversion explains how far the decimal point moves and why. Significant figures are kept as you typed them, or rounded to the number you choose.
In Calculate mode, add, subtract, multiply or divide two numbers and follow the method: multiply the coefficients and add the exponents, divide and subtract, or match the powers of ten before adding. The answer follows the significant-figure rules, keeps every digit, or uses the number of figures you pick. The arithmetic is exact — there is no floating-point rounding.
How to use it
- Type or paste a number. Write powers of ten as
4.5e-4,4.5E-4,4.5 × 10^-4,4.5x10^-4or4.5 × 10⁻⁴; SI prefixes can be symbols (4.7 k,220 µor220 u) or names (3 mega). - Choose Significant figures: As entered keeps the figures you typed; a number rounds to that many (a dropped 5 rounds up).
- Read the results — scientific, E and engineering notation, the SI prefix and the number written out — and copy any of them, or use Copy all.
- For arithmetic, switch to Calculate, enter two numbers, choose + − × ÷ and how many significant figures the answer should have.
Examples
299792458
2.99792458 × 10⁸ = 299.792458 × 10⁶ = 299.792458 M
The decimal point moves 8 places to the left, so the exponent is 8.
0.00045
4.5 × 10⁻⁴ = 450 × 10⁻⁶ = 450 µ
The decimal point moves 4 places to the right, so the exponent is −4.
6.022e23
6.022 × 10²³ = 602,200,000,000,000,000,000,000
(3.0 × 10⁴) × (2.5 × 10⁻²)
7.5 × 10²
3.0 × 2.5 = 7.5 and 4 + (−2) = 2.
(4.5 × 10⁵) + (3.2 × 10⁴)
4.8 × 10⁵
Rewrite 3.2 × 10⁴ as 0.32 × 10⁵ and add: 4.5 + 0.32 = 4.82. By the significant-figure rules the answer is rounded to the 10⁴ place, the precision of 4.5 × 10⁵.
Common uses
- Checking chemistry, physics and maths homework that uses powers of ten.
- Reading calculator or spreadsheet results such as 1.2E-05.
- Writing component values such as 4.7 kΩ or 220 µF as powers of ten, and back.
Scientific, E and engineering notation
- Scientific notation writes a number as a × 10ⁿ with 1 ≤ |a| < 10: 4,500 = 4.5 × 10³ and 0.0045 = 4.5 × 10⁻³.
- E notation is the same thing in plain text: 4.5E3 or 4.5e-3. Calculators, spreadsheets and programming languages use it.
- Engineering notation only uses powers of ten that are multiples of 3, so 1 ≤ |a| < 1000: 45,000 = 45 × 10³. Each of those powers has an SI prefix, so 45 × 10³ can be written 45 k.
In the UK and many other countries, standard form means scientific notation. In the US, standard form usually means the number written out in full (4,500). The tool shows both.
Calculating in scientific notation
- Multiply: multiply the coefficients and add the exponents: (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹.
- Divide: divide the coefficients and subtract the exponents: (6 × 10⁵) ÷ (2 × 10²) = 3 × 10³.
- Add or subtract: first rewrite the numbers with the same power of ten, then add or subtract the coefficients: 4.5 × 10⁵ + 3.2 × 10⁴ = 4.5 × 10⁵ + 0.32 × 10⁵ = 4.82 × 10⁵.
- Tidy up: if the coefficient is 10 or more, or less than 1, move its decimal point and change the exponent to match: 20 × 10⁵ = 2.0 × 10⁶.
SI prefixes
The International System of Units (SI) has 24 prefixes, from quecto (q, 10⁻³⁰) to quetta (Q, 10³⁰), listed in the BIPM SI Brochure. Ronna (R, 10²⁷), quetta, ronto (r, 10⁻²⁷) and quecto were added by the 27th General Conference on Weights and Measures in November 2022. Prefix symbols are case-sensitive — m is milli (10⁻³) but M is mega (10⁶) — and the micro sign is µ (type u if your keyboard has no µ). The full list is under All SI prefixes in the tool.
Limitations
- Numbers can have up to 100 digits and powers of ten from −10,000 to 10,000. The number is only written out in full when that takes 400 characters or fewer.
- Rounding to a chosen number of significant figures rounds a dropped 5 up (away from zero). For the round-half-to-even rule, use the significant figures calculator.
- Units are not converted: type the prefix on its own (4.7 k, not 4.7 kΩ). For unit conversions use the unit converter.
- Calculate mode works on two numbers at a time.
Privacy
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Frequently asked questions
How do I convert a number to scientific notation?
Move the decimal point until exactly one non-zero digit is in front of it. The number of places you moved it is the exponent — positive if you moved it left (large numbers), negative if you moved it right (small numbers). 4,500 = 4.5 × 10³ and 0.0045 = 4.5 × 10⁻³.
What does 1.5E-7 mean?
It is E notation for 1.5 × 10⁻⁷, which is 0.00000015. The E means “times ten to the power of”. Calculators and spreadsheets use it when a number is too long to display.
What is the difference between scientific and engineering notation?
Scientific notation keeps one digit before the decimal point (1 ≤ |a| < 10). Engineering notation allows one to three digits so that the exponent is a multiple of 3 (1 ≤ |a| < 1000), which matches the SI prefixes: 4.7 × 10⁴ = 47 × 10³ = 47 k.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then tidy up if the coefficient is 10 or more: (5 × 10³) × (4 × 10²) = 20 × 10⁵ = 2 × 10⁶.
How do you add numbers in scientific notation?
Rewrite them with the same exponent first: 4.5 × 10⁵ + 3.2 × 10⁴ = 4.5 × 10⁵ + 0.32 × 10⁵ = 4.82 × 10⁵. With significant-figure rules, round to the precision of the less precise number: 4.8 × 10⁵.
What are the newest SI prefixes?
Ronna (R, 10²⁷), quetta (Q, 10³⁰), ronto (r, 10⁻²⁷) and quecto (q, 10⁻³⁰), adopted in November 2022. Before that the largest and smallest prefixes were yotta (10²⁴) and yocto (10⁻²⁴).
Is standard form the same as scientific notation?
In the UK and many other countries, yes — standard form means a × 10ⁿ. In the US, standard form usually means the number written out in full (4,500). This tool shows both.