About the Scientific Notation Calculator
This scientific notation calculator converts any number into scientific notation (standard form), E notation and engineering notation, and turns numbers written as a × 10ⁿ back into ordinary decimals. You can type values in almost any format — 0.000045678, 6.022e23, 6.022 × 10^23 or 3.2x10^-5 — and choose how many significant figures to keep.
It also does arithmetic: pick add, subtract, multiply, divide or power and enter a second number to get the answer directly in scientific notation. That makes it useful for chemistry (Avogadro’s number, molar quantities), physics (the speed of light, Planck’s constant), astronomy distances, electronics component values and any homework where numbers are very large or very small.
Engineering notation is shown alongside, with the exponent always a multiple of three so it lines up with SI prefixes such as kilo, mega, milli and micro. The “Auto” setting keeps every significant digit of the input; choose a fixed number of significant figures to round the mantissa.
How to use the scientific notation calculator
- 1Type a number in decimal, E notation or a × 10^n form.
- 2Leave the operation on “Convert only”, or choose +, −, ×, ÷ or ^ and enter a second number.
- 3Pick how many significant figures to keep, or leave it on Auto.
- 4Read the scientific, E, engineering and decimal forms of the result.
Formula and method
A number is in scientific notation when it is written as a coefficient a with exactly one non-zero digit before the decimal point, multiplied by a power of ten. The exponent n is the number of places the decimal point moves: positive for large numbers, negative for numbers smaller than one. E notation writes the same thing as aEn (for example 6.022e23), which is how calculators and spreadsheets display it.
Engineering notation uses exponents that are multiples of three, so the coefficient is between 1 and 1,000. For arithmetic: multiply the coefficients and add the exponents; divide the coefficients and subtract the exponents; to add or subtract, first rewrite both numbers with the same exponent. The result is then normalised back to 1 ≤ |a| < 10.
- a
- Coefficient (mantissa), 1 ≤ |a| < 10
- n
- Integer exponent — the power of ten
- E
- Shorthand for “× 10^” in E notation
Worked examples
Speed of light in standard form
299,792,458 m/s has 9 digits, so the decimal point moves 8 places left: 2.99792458 × 10⁸. In engineering notation that is 299.792458 × 10⁶ (mega).
Small number rounded to 3 significant figures
Moving the decimal point 5 places right gives 4.5678, so the exponent is −5. Rounded to 3 significant figures the coefficient is 4.57, giving 4.57 × 10⁻⁵, or 45.7 × 10⁻⁶ (micro) in engineering form.
Multiply (3.2 × 10⁵) × (4 × 10⁻²)
Multiply the coefficients (3.2 × 4 = 12.8) and add the exponents (5 + (−2) = 3) to get 12.8 × 10³, then normalise to 1.28 × 10⁴ = 12,800.
Divide Avogadro’s number by 1,000
Dividing by 1,000 = 10³ subtracts 3 from the exponent: 6.022 × 10²³ ÷ 10³ = 6.022 × 10²⁰.
Frequently asked questions
How do you convert a number to scientific notation?+
Move the decimal point until exactly one non-zero digit is to its left. Count how many places you moved it: that count is the exponent, positive if you moved left (big numbers) and negative if you moved right (small numbers). For example 4,500 = 4.5 × 10³.
What is the difference between scientific and engineering notation?+
Scientific notation keeps the coefficient between 1 and 10. Engineering notation keeps it between 1 and 1,000 so the exponent is always a multiple of 3, matching SI prefixes like kilo (10³), mega (10⁶) and micro (10⁻⁶).
What does E mean in a number like 3.5E-7?+
E stands for “times ten to the power of”. 3.5E-7 means 3.5 × 10⁻⁷ = 0.00000035. Calculators, spreadsheets and programming languages use E notation because it is easy to type.
How do you multiply numbers in scientific notation?+
Multiply the coefficients and add the exponents, then adjust if the coefficient is 10 or more. For example (2 × 10⁴) × (6 × 10³) = 12 × 10⁷ = 1.2 × 10⁸.
Is scientific notation the same as standard form?+
In the UK and many other countries, “standard form” means scientific notation (a × 10ⁿ with 1 ≤ a < 10). In US schools, “standard form” often means the ordinary decimal way of writing a number instead.
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