Scientific Notation Calculator
Scientific Notation Converter
Enter a value below and the tool will display it in scientific, engineering, E‑notation and plain decimal forms. Acceptable inputs include formats such as 3672.2, 2.3e11 or 3.5×10⁻¹².
Scientific Notation Calculator
Use the calculator below to perform calculations using scientific notation.
Scientific notation
Scientific notation expresses numbers as a coefficient multiplied by a power of ten, which is handy for handling extremely large or tiny quantities. It is widely employed in maths, engineering and the sciences to simplify calculations. In this format a number appears as a base b (the significand) times 10 raised to an integer exponent n, the order of magnitude.
b × 10n
Below are some examples of numbers written in decimal notation compared to scientific notation:
| Decimal notation | Scientific notation |
| 5 | 5 × 100 |
| 700 | 7 × 102 |
| 1,000,000 | 1 × 106 |
| 0.0004212 | 4.212 × 10-4 |
| -5,000,000,000 | -5 × 109 |
Calculations with scientific notation
Scientific notation can simplify the process of computing basic arithmetic operations by hand.
Addition and subtraction:
When adding or subtracting numbers written in scientific notation, first rewrite each term so that they share the same power of ten. For instance, 100 can be shown as 1 × 102, 0.01 as 1 × 10-2, 0.0001 as 1 × 10-4, etc. Once the exponents match, the coefficients can be combined. Example: 1.432 × 102 + 800 × 10-1 – 0.001 × 105:
| 1.432×102 + 800×10-1 – 0.001×105 | |
| = | 1.432×102 + 0.8×102 – 1×102 |
| = | (1.432 + 0.8 – 1)×102 |
| = | 1.232×102 |
Multiplication:
To multiply values in scientific notation, keep the coefficients separate from the powers of ten. Multiply the coefficients in the usual way and add the exponents of ten to obtain the new exponent. For example: 1.432 × 102 × 800 × 10-1 × 0.001 × 105:
1.432 × 800 × 0.001 = 1.1456
102 × 10-1 × 105 = 102+(-1)+5 = 106
Thus:
1.432×102 × 800×10-1 × 0.001×105 = 1.1456×106
Division:
Division in scientific notation works by dividing the coefficients normally and subtracting the exponent of the divisor from the exponent of the dividend. The result is usually expressed with a single non‑zero digit to the left of the decimal point. Example: (1.432 × 102) ÷ (800 × 10-1) ÷ (0.001 × 105):
1.432 ÷ 800 ÷ 0.001 = 1.79
102 ÷ 10-1 ÷ 105 = 10(2-(-1)-5) = 10-2
Thus:
(1.432×102) ÷ (800×10-1) ÷ (0.001×105) = 1.79×10-2
If, for example, the solution had instead been 0.179×10-2, by convention, we would shift the decimal to the left such that the first digit left of the decimal point wouldn't be 1, then change the exponent accordingly:
0.179×10-2 = 1.79×10-3
Engineering notation
Engineering notation resembles scientific notation, but forces the exponent n to be a multiple of three (…, ‑6, ‑3, 0, 3, 6, 9, …). This aligns the value with SI prefixes such as kilo (103), mega (106) or giga (109). Converting from scientific to engineering simply shifts the decimal point so the exponent meets this rule.
1.234 × 108 (scientific notation)
can be converted to:
123.4 × 106 (engineering notation)
E-notation
E‑notation is essentially scientific notation where the “× 10” factor is replaced by the letter “E”. It is handy when the exponent cannot be displayed as a superscript. The format looks like:
bEn
where b is the base, E indicates "x 10" and the n is written after the E. Below is a comparison of scientific notation and E-notation:
| Scientific notation | E-notation |
| 5 × 100 | 5E0 |
| 7 × 102 | 7E2 |
| 1 × 106 | 1E6 |
| 4.212 × 10-4 | 4.212E-4 |
| -5 × 109 | -5E9 |
The calculator accepts both capital “E” and lowercase “e” as the exponent marker. Different programming environments may use alternative representations, but the underlying concept is the same.