Scientific notation calculator
Type a number in any form, get it in scientific notation and back.
How do I write a number in scientific notation?
Move the decimal point until one non-zero digit is left of it, and count the moves: 123,000 = 1.23 × 10⁵ (five places left), 0.00056 = 5.6 × 10⁻⁴ (four places right).
How do I convert scientific notation back to a regular number?
Move the decimal point by the exponent — right for positive, left for negative: 4.56 × 10⁻³ = 0.00456, and 7.2 × 10⁶ = 7,200,000.
What is E notation?
The same thing written for calculators and spreadsheets: 1.23E5 means 1.23 × 10⁵, and 5.6E-4 means 5.6 × 10⁻⁴. You can type either form here.
What is engineering notation?
Scientific notation with the exponent a multiple of 3, so it lines up with kilo, mega, milli and micro: 0.00056 = 560 × 10⁻⁶ (560 micro-), 123,000 = 123 × 10³ (123 kilo-).
How do I multiply numbers in scientific notation?
Multiply the front numbers and add the exponents: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. If the front number reaches 10 or more, shift it: 5 × 10² × 4 × 10³ = 20 × 10⁵ = 2 × 10⁶.
How many significant figures does a number have?
Count the digits from the first non-zero digit. 0.00450 has 3 significant figures, 1,200. (with a decimal point) has 4, and 1,200 with no point is ambiguous: it could have 2 to 4. Writing 1.2 × 10³ or 1.200 × 10³ removes the doubt.
The form and why it is used
A number in scientific notation is written m × 10ᵉ, with 1 ≤ |m| < 10 and e an integer. The exponent says how many places the decimal point moves, and the digits of m carry the significant figures. This keeps very large and very small quantities compact and shows the precision directly. Engineering notation restricts the exponent to a multiple of three so that it matches the SI prefixes: kilo (10³), mega (10⁶), milli (10⁻³) and micro (10⁻⁶).
Worked examples
The speed of light, 299,792,458 m/s, is 2.99792458 × 10⁸ m/s in scientific notation. Avogadro’s constant, written as 6.02214076e23 in E notation, is 6.02214076 × 10²³ per mole, which has 9 significant figures. A wavelength of 1.5e-7 m is 1.5 × 10⁻⁷ m, or 150 × 10⁻⁹ m in engineering notation, which is 150 nanometers. To add numbers, first give them the same exponent: 3 × 10⁴ + 5 × 10³ = 3 × 10⁴ + 0.5 × 10⁴ = 3.5 × 10⁴. To divide, divide the front numbers and subtract the exponents: (6 × 10⁸) ÷ (3 × 10³) = 2 × 10⁵.
Common mistakes
Moving the decimal point the wrong way is the most frequent error: a bigger number has a positive exponent, a number below 1 has a negative one. Adding the exponents when adding the numbers is the second; exponents are added only in multiplication. A third is leaving a front number outside the range 1 to 10 after a calculation, as in 20 × 10⁵, which should be rewritten as 2 × 10⁶. In E notation, the E means “times ten to the power”, and it is not Euler’s number e ≈ 2.718.
Sources: NIST Guide for the Use of the International System of Units (SP 811), including the rules for significant figures and SI prefixes; OpenStax Chemistry 2e, Essential Skills 1 (exponential notation). The speed of light and Avogadro’s constant are exact values defined in the 2019 SI. Related: significant figures calculator, rounding calculator, exponent calculator and scientific calculator.