Scientific Notation Calculator
Rewrite very large or very small numbers as a × 10ⁿ, or expand them back to ordinary decimals.
How to use the Scientific Notation Calculator
- Enter the number – Also accepts 4.5e-5 or 4.5 x 10^-5.
- Press Calculate. The result updates automatically as you type.
About the Scientific Notation Calculator
Scientific notation keeps very large and very small numbers readable. The distance to the Sun, about 150,000,000 km, becomes 1.5 × 10⁸ km, and the mass of a proton, 0.00000000000000000000000000167 kg, becomes 1.67 × 10⁻²⁷ kg. It also makes the precision of a measurement clear, since every digit in the coefficient is significant.
E notation (4.5E-5) is how calculators, spreadsheets and programming languages print the same thing. Engineering notation is handy in electronics and physics because the exponent maps straight onto a metric prefix: 45 × 10⁻⁶ A is 45 µA. Trailing zeros you type in a whole number are not treated as significant here; write 4.50e3 if you mean three significant figures.
Formula
N = a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer
Move the decimal point until one non-zero digit is left of it. The number of places moved is n: positive if you moved left (large numbers), negative if you moved right (small numbers). Engineering notation restricts n to multiples of 3, matching the prefixes kilo, mega, milli and micro.
Example calculation
Using the default values:
- Number = 0.000045
the calculator returns:
- Scientific notation: 4.5 × 10^-5
- E notation: 4.5E-5
- Engineering notation: 45 × 10^-6
- Decimal notation: 0.000045
- Significant figures shown: 2
Frequently asked questions
How do I write 0.000045 in scientific notation?
Move the decimal point 5 places right to get 4.5, so the exponent is −5: 4.5 × 10⁻⁵.
What does 3.2E6 mean?
It is E notation for 3.2 × 10⁶, which equals 3,200,000.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then renormalize. (3 × 10⁴)(5 × 10³) = 15 × 10⁷ = 1.5 × 10⁸.
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