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Convert any number to scientific notation, engineering notation or E notation, or add, subtract, multiply and divide numbers like 6.4 × 10⁵ with every step shown. Exact digits, no floating-point rounding.
Quick answer: Scientific notation writes a number as a × 10n, where a is at least 1 and less than 10, and n is a whole number. 45,600 is 4.56 × 104, and 0.00072 is 7.2 × 10−4.
Calculations use exact integer arithmetic on the digits you type, so long numbers are not rounded by floating-point errors.
| Standard form | Scientific notation | Decimal point moved |
|---|---|---|
| 45,600 | 4.56 × 104 | 4 places left |
| 3,000,000 | 3 × 106 | 6 places left |
| 0.00072 | 7.2 × 10−4 | 4 places right |
| 0.000000015 | 1.5 × 10−8 | 8 places right |
| 602,200,000,000,000,000,000,000 | 6.022 × 1023 | 23 places left |
| 7.5 | 7.5 × 100 | none |
Multiply the coefficients and add the exponents. (3 × 104) × (2 × 103) = 6 × 107. If the coefficient ends up at 10 or more, move the decimal and raise the exponent: (8 × 105) × (5 × 102) = 40 × 107 = 4 × 108.
Divide the coefficients and subtract the exponents. (6.4 × 105) ÷ (1.6 × 102) = 4 × 103.
Rewrite both numbers with the same power of ten, then add or subtract the coefficients. (5 × 103) + (3 × 102) = 5 × 103 + 0.3 × 103 = 5.3 × 103. And (7.5 × 104) − (2.5 × 103) = 7.5 × 104 − 0.25 × 104 = 7.25 × 104.
To raise to a power, raise the coefficient to that power and multiply the exponent: (2 × 103)2 = 4 × 106. For a square root of a number with an odd exponent, first shift to an even one: √(9 × 105) = √(90 × 104) ≈ 9.49 × 102.
| Style | Rule | Example for 45,600 |
|---|---|---|
| Scientific notation | Coefficient from 1 up to (not including) 10 | 4.56 × 104 |
| Engineering notation | Exponent is a multiple of 3, coefficient from 1 to 999.99… | 45.6 × 103 |
| E notation | Calculator and spreadsheet text form; E means “× 10 to the power” | 4.56E+4 |
| Standard (decimal) form | Ordinary digits | 45,600 |
Engineering notation lines up with SI prefixes: 103 is kilo, 106 mega, 109 giga, 1012 tera, 10−3 milli, 10−6 micro, 10−9 nano and 10−12 pico.
| Quantity | Standard value | Scientific notation |
|---|---|---|
| Speed of light in a vacuum | 299,792,458 m/s (exact) | 2.99792458 × 108 m/s |
| Avogadro constant | 602,214,076,000,000,000,000,000 per mole (exact) | 6.02214076 × 1023 mol−1 |
| Planck constant | 0.000…000662607015 J·s (exact) | 6.62607015 × 10−34 J·s |
| Elementary charge | 0.000…0001602176634 C (exact) | 1.602176634 × 10−19 C |
| 1 astronomical unit | 149,597,870,700 m (exact) | 1.495978707 × 1011 m |
| Mass of Earth | about 5,972,000,000,000,000,000,000,000 kg | ≈ 5.972 × 1024 kg |
| Mass of an electron | about 0.00000000000000000000000000000091094 kg | ≈ 9.109 × 10−31 kg |
The first four are defined values in the 2019 SI system; the last two are measured, so they are shown to four significant figures.
Every digit in the coefficient is significant, which is why scientific notation is the clearest way to show precision. 3.20 × 104 has three significant figures, while 3.2 × 104 has two. In a plain whole number such as 32,000 the trailing zeros are normally treated as placeholders, so it has two significant figures. A decimal such as 0.00450 has three: leading zeros never count, but the trailing zero after the 5 does. This calculator counts the digits you type and keeps trailing zeros when the number contains a decimal point.
Scientific notation is a way to write very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of ten, such as 6.02 × 10²³ or 1.6 × 10⁻¹⁹.
Move the decimal point 4 places to the right to get 4.5, and use a negative exponent: 4.5 × 10⁻⁴.
Move the decimal point 7 places to the left to get 4.5, so 45,000,000 = 4.5 × 10⁷.
E means “times ten to the power of”. So 3.2E5 is 3.2 × 10⁵ = 320,000, and 3.2E-5 is 3.2 × 10⁻⁵ = 0.000032.
It makes every number have one standard form, so numbers are easy to compare: the exponent shows the size, and the coefficient shows the detail. 45 × 10³ and 4.5 × 10⁴ are equal, but only the second is in proper scientific notation.
A negative exponent means the number is less than 1. 10⁻³ is 1/1,000 = 0.001, so 5 × 10⁻³ = 0.005.
Rewrite them with the same exponent, add the coefficients, then adjust to a coefficient between 1 and 10. For example, 5 × 10³ + 3 × 10² = 5.3 × 10³.
Multiply the coefficients and add the exponents. (3 × 10⁴) × (2 × 10³) = 6 × 10⁷.
Zero is written as 0 × 10⁰, because it has no non-zero leading digit.
In engineering notation the exponent is always a multiple of 3, so 45,600 becomes 45.6 × 10³ instead of 4.56 × 10⁴. This matches SI prefixes such as kilo, mega and milli.
Defined constants follow the 2019 SI redefinition (see NIST SP 811) and the International Astronomical Union’s 2012 definition of the astronomical unit; measured values are rounded to four significant figures. Every worked example on this page was recalculated against the rules shown, and the calculator uses exact integer arithmetic. See our editorial policy for how we build and review tools.