Scientific Notation Calculator
Convert any number to scientific notation and back, round it to significant figures, or add, subtract, multiply and divide numbers written as a × 10ⁿ.
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Standard (123000), E notation (1.23e5) or scientific (1.23 × 10^5).
Leave empty to keep the figures you typed.
- Standard form (decimal)
- 0.000450
- E notation
- 4.50e-4
- Engineering notation
- 450 × 10⁻⁶
- Coefficient
- 4.50
- Exponent
- -4
- Significant figures
- 3
How this was calculated
- Move the decimal point so exactly one non-zero digit is to its left: 4.50.
- The point moved 4 places to the right, so the exponent is negative: -4.
- Result: 4.50 × 10⁻⁴.
Scientific notation arithmetic
How this was calculated
- 3.0 × 10⁴ × 2.0 × 10⁻²
- Multiply the coefficients and add the exponents: (3 × 2) × 10^(4 + -2) = 6 × 10².
- Normalize so the coefficient is between 1 and 10 and round to 2 significant figures: 6.0 × 10².
How this scientific notation calculator works
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten: a × 10n. It keeps very large and very small numbers readable (the speed of light is 3.00 × 108 m/s, a hydrogen atom is about 1.1 × 10−10 m wide) and makes the significant figures obvious. This scientific notation calculator converts in both directions, shows E and engineering notation, rounds to any number of significant figures, and does arithmetic on two numbers with the sig-fig rules applied.
It works on the digits you type rather than on a rounded floating-point number, so 0.000450 keeps its trailing zero (three significant figures) and very long numbers are converted exactly.
Converting, with examples
Standard to scientific: move the decimal point until one non-zero digit is left of it and count the moves. Left moves give a positive exponent, right moves a negative one. 123,000 → 1.23 × 105 (five places left). 0.000450 → 4.50 × 10−4 (four places right).
Scientific to standard: move the point the other way. 6.02 × 1023 has 23 places to the right, giving 602 followed by 21 zeros. 4.5 × 10−5 is 0.000045. In E notation, used by calculators and spreadsheets, the same numbers are 6.02e23 and 4.5e-5.
Multiplying, dividing, adding and subtracting
To multiply, multiply the coefficients and add the exponents: (3.0 × 104)(2.0 × 10−2) = 6.0 × 102. To divide, divide the coefficients and subtract the exponents. To add or subtract, first rewrite both numbers with the same exponent: 1.2 × 103 + 3.4 × 102 = 1.2 × 103 + 0.34 × 103 = 1.54 × 103. Finally renormalize if the coefficient is 10 or more (12 × 103 becomes 1.2 × 104).
Significant figures follow the usual chemistry and physics rules. For × and ÷ the answer keeps as many significant figures as the least precise input. For + and −, it keeps the least precise decimal place, which is why 1.2 × 103 + 3.4 × 102 is reported as 1.5 × 103.
Common mistakes
- Coefficient out of range. 45 × 103 is not normalized; it should be 4.5 × 104. (Engineering notation is the exception: it deliberately uses exponents that are multiples of 3.)
- Wrong exponent sign. Numbers smaller than 1 have negative exponents. 0.005 is 5 × 10−3, not 5 × 103.
- Dropping meaningful zeros. 2.50 × 103 (three sig figs) and 2.5 × 103 (two) are different measurements.
When the result is misleading
Whole numbers with trailing zeros are ambiguous: 1,500 could have two, three or four significant figures. The calculator treats them as not significant unless you write a decimal point (1500. or 1.500e3). Sig-fig rounding is also a convention for reporting measurements, not a law of math; keep extra digits in intermediate steps and round only the final answer. For statistics on a data set, see the standard deviation calculator.
Frequently asked questions
How do you write a number in scientific notation?
Move the decimal point until exactly one non-zero digit is left of it, and count the moves. 123,000 becomes 1.23 × 10⁵ (moved 5 places left) and 0.00045 becomes 4.5 × 10⁻⁴ (moved 4 places right).
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then renormalize. (3 × 10⁴)(2 × 10⁻²) = 6 × 10². If the coefficient comes out 10 or more, shift it: 12 × 10³ = 1.2 × 10⁴.
How do you add numbers in scientific notation?
Rewrite them with the same exponent first, then add the coefficients. 1.2 × 10³ + 3.4 × 10² = 1.2 × 10³ + 0.34 × 10³ = 1.54 × 10³, which rounds to 1.5 × 10³ with correct significant figures.
What is E notation?
The calculator and spreadsheet form of scientific notation: 6.02e23 means 6.02 × 10²³ and 4.5e-4 means 4.5 × 10⁻⁴.
What is engineering notation?
Scientific notation with the exponent restricted to multiples of 3, so it lines up with prefixes like kilo, mega and micro. 0.000045 is 45 × 10⁻⁶ (45 micro).