Scientific Notation Calculator
Scientific Notation1.23457 × 10^5
Engineering Notation123.457 × 10^3
Standard Form123456.789
Scientific notation expresses very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of ten, making them compact and easy to compare. This calculator converts any finite number into both scientific notation and engineering notation, and reports the coefficient and exponent separately for use in further work.
Formula
value = c × 10^e, where e = floor(log10(|value|)) and c = |value| / 10^e (sign applied to c)
- value
- The number being converted (any finite number; 0 maps to 0)
- c
- Coefficient, normally between 1 and 10, shown to 6 significant digits
- e
- Exponent of ten; in engineering notation it is rounded down to the nearest multiple of 3
How it works
- Enter any finite number — a tiny fraction like 0.00045 or a large value like 123456.
- The calculator finds the exponent as the floor of log10 of the absolute value, then divides by that power of ten to get a coefficient, which is shown to six significant digits.
- It also produces engineering notation, where the exponent is forced to a multiple of three (matching SI prefixes like kilo, milli, and micro), and reports the standard decimal form, coefficient, and exponent.
Worked examples
Convert 0.00045 to scientific and engineering notation.
- Absolute value 0.00045; log10 ≈ −3.35, floor = −4, so the exponent is −4.
- Coefficient = 0.00045 / 10^−4 = 4.5, shown as 4.50000.
- For engineering form the exponent drops to the nearest multiple of 3 (−6), giving 450.000.
Scientific: 4.50000 × 10^-4 ; Engineering: 450.000 × 10^-6
Convert 123456 to scientific and engineering notation.
- log10(123456) ≈ 5.09, floor = 5, so the exponent is 5.
- Coefficient = 123456 / 10^5 = 1.23456.
- Engineering form uses exponent 3, giving 123.456 × 10^3.
Scientific: 1.23456 × 10^5 ; Engineering: 123.456 × 10^3
Frequently asked questions
- What is the difference between scientific and engineering notation?
- Scientific notation keeps the coefficient between 1 and 10, so the exponent can be any integer. Engineering notation forces the exponent to a multiple of three so it lines up with SI prefixes like kilo (10^3), milli (10^-3), and micro (10^-6), letting the coefficient range up to 1000.
- How many digits does the coefficient show?
- The coefficient is displayed to six significant digits using fixed precision, so 4.5 appears as 4.50000. This keeps outputs consistent and avoids floating-point noise in the trailing places.
- How is zero handled?
- Zero is a special case: it cannot be written as a nonzero coefficient times a power of ten, so the calculator simply returns 0 for the scientific form, engineering form, and standard form with a coefficient and exponent of 0.
- Can it convert negative numbers?
- Yes. The sign is preserved on the coefficient, so −123456 becomes −1.23456 × 10^5. The exponent is computed from the absolute value, and only non-finite inputs (infinity or NaN) are rejected.