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Scientific Notation Calculator
Type a number in any common style, such as 123456, 0.00045, 1.5e-3 or 4.5 × 10^6, and see it as scientific notation, E notation, engineering notation and an ordinary decimal.
What scientific notation looks like
Scientific notation writes a number as a × 10n, where the coefficient a satisfies 1 ≤ |a| < 10 and the exponent n is a whole number. The speed of light, about 299,792,458 m/s, becomes 2.99792458 × 108, and a length of 0.00045 m becomes 4.5 × 10−4. The notation keeps very large and very small values short and makes the size of a number obvious from its exponent alone.
To convert by hand, move the decimal point until exactly one non-zero digit sits to its left. Count the places moved: moving left gives a positive exponent, moving right gives a negative one. To reverse the process, move the point the number of places the exponent indicates, padding with zeros.
E notation and engineering notation
Calculators, spreadsheets and programming languages write the same value as 4.5e-4, where the letter e means "times ten to the power". It has nothing to do with Euler's number. Engineering notation is a variant that restricts the exponent to multiples of three, so the coefficient can run from 1 up to 999. It lines up with the SI prefixes.
| Prefix | Power of ten | Prefix | Power of ten |
|---|---|---|---|
| kilo | 103 | milli | 10−3 |
| mega | 106 | micro | 10−6 |
| giga | 109 | nano | 10−9 |
| tera | 1012 | pico | 10−12 |
So 0.00045 in engineering form is 450 × 10−6, which reads as 450 micro-units.
Calculating with 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 × 109) ÷ (2 × 105) = 3 × 104.
- Add or subtract: first rewrite both numbers with the same exponent, then combine the coefficients. 3 × 104 + 5 × 103 = 3.5 × 104.
After a calculation, renormalise the result if the coefficient falls outside 1 to 10; for example 12 × 103 becomes 1.2 × 104.
Trailing zeros and significant digits
This page keeps the digits you type when a decimal point or an exponent is present, so 1.50e3 stays 1.50 × 103 with three significant digits. For a plain whole number such as 1500 the trailing zeros are ambiguous (they may be placeholders), so they are dropped and the result is 1.5 × 103. If those zeros are measured digits, enter the number as 1.500e3 or 1500. instead. The significant figures calculator explains the counting rules in detail, and the exponent calculator handles powers directly. A negative sign is carried through every form, and zero is written as 0 × 100.
Worked example
Write the small number 0.00045 in scientific notation by counting how far the decimal point moves to the right.
Inputs
| Number | 0.00045 |
|---|
Result
Scientific notation: one non-zero digit before the point, times a power of ten.
| Scientific notation | 4.5 × 10^-4 |
|---|---|
| E notation | 4.5e-4 |
| Engineering notation | 450 × 10^-6 |
| Standard (decimal) form | 0.00045 |
| Order of magnitude | 10^-4 |
| Significant digits shown | 2 |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How do I write a number in scientific notation?
Move the decimal point until one non-zero digit remains before it, then multiply by 10 raised to the number of places moved. The exponent is positive if you moved left and negative if you moved right.
What does the e in 1.5e3 mean?
It stands for "times ten to the power of", so 1.5e3 means 1.5 × 10^3, which is 1,500. It is a keyboard-friendly way to write scientific notation.
What is the difference between scientific and engineering notation?
Scientific notation always has a coefficient between 1 and 10. Engineering notation keeps the exponent a multiple of three, so the coefficient is between 1 and 999.
How do I convert scientific notation back to a normal number?
Move the decimal point right for a positive exponent or left for a negative one, adding zeros as needed. For example, 4.5 × 10^6 becomes 4,500,000.
Why is zero written as 0 × 10^0?
Zero has no non-zero leading digit to place before the decimal point, so no exponent can normalise it. By convention it is written with an exponent of zero.
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References and sources
- NIST Guide for the Use of the International System of Units (SI), Special Publication 811: SI prefixes and powers of ten. Link
- ISO 80000-1: Quantities and units, general principles, for writing numbers and units.