Scientific notation calculator (and engineering notation)
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Result
Convert a number to scientific notation, E notation and engineering notation with its SI prefix, or back to an ordinary decimal. You can also add, subtract, multiply and divide two numbers written in scientific notation: the calculator shows how the coefficients and the powers of ten are combined and normalised, and rounds the answer to the right number of significant figures.
Step-by-step solution
Move the decimal point
Engineering notation and SI prefix
Key formulas
- Scientific notation
- a × 10n, 1 ≤ |a| < 10
- Multiplying
- (a × 10m)·(b × 10n) = ab × 10m+n
- Dividing
- (a × 10m)/(b × 10n) = (a/b) × 10m−n
- Adding
- write both with the same power of ten first
How to write a number in scientific notation
- Move the decimal point until exactly one non-zero digit is in front of it: 0.000345 becomes 3.45.
- Count how many places the point moved. Moving it to the left makes the power of ten positive, to the right makes it negative: 0.000345 = 3.45 × 10⁻⁴.
- To multiply, multiply the coefficients and add the exponents. To divide, divide the coefficients and subtract the exponents.
- To add or subtract, first rewrite both numbers with the same power of ten, then add or subtract the coefficients.
- Normalise the result so the coefficient is at least 1 and less than 10: 18.06 × 10¹⁸ = 1.806 × 10¹⁹.
- For engineering notation choose a power of ten that is a multiple of 3, so it matches an SI prefix: 3.45 × 10⁻⁴ = 345 × 10⁻⁶, or 345 µ.
Questions and answers
What is E notation?
A way to type scientific notation on calculators and computers: 6.02E23 means 6.02 × 10²³ and 3.45E-4 means 3.45 × 10⁻⁴. The E stands for exponent, not for Euler’s number e.
What is the difference between scientific and engineering notation?
In scientific notation the coefficient is between 1 and 10. In engineering notation the exponent is a multiple of 3 and the coefficient is between 1 and 1000, so the number can be read with an SI prefix: 4.7 × 10³ Ω is 4.7 kΩ and 2.2 × 10⁻⁸ F is 22 nF.
Which SI prefixes are there?
From large to small: quetta (Q, 10³⁰), ronna (R, 10²⁷), yotta (Y), zetta (Z), exa (E), peta (P), tera (T), giga (G), mega (M), kilo (k), then milli (m), micro (µ), nano (n), pico (p), femto (f), atto (a), zepto (z), yocto (y), ronto (r) and quecto (q, 10⁻³⁰), each a factor of 1000 apart.
How many significant figures does a number in scientific notation have?
All the digits of the coefficient: 4.50 × 10³ has three. That is why scientific notation removes the ambiguity of numbers such as 4500.
Practise it yourself
Practise Number systems
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