Exponential Notation Calculator
Enter any number and this calculator converts it to scientific notation (a x 10^n), E notation, and engineering notation in one click. Choose your significant figures, see the full step-by-step breakdown, and switch between conversion and arithmetic modes to add, subtract, multiply, or divide numbers already in exponential form.
What is exponential notation?
Exponential notation is a compact way to write any number as a product of a coefficient and a power of ten: N = a x 10^n. The coefficient (a) holds the significant digits, and the exponent (n) tells you how many places the decimal point must move to reach the original number. A positive exponent means the number is large; a negative exponent means it is a small fraction. For example, 52,000 becomes 5.2 x 10^4 because the decimal moves four places to the left, and 0.000052 becomes 5.2 x 10^-5 because it moves five places to the right.
Scientific notation vs. E notation vs. engineering notation
These three formats all express the same idea but differ in convention. Scientific notation (5.2 x 10^4) requires the coefficient to be between 1 and 10, giving exactly one non-zero digit before the decimal point. E notation (5.2E4) is identical in value but replaces "x 10^" with the letter E, which is convenient for keyboards and code. Engineering notation relaxes the rule so that the exponent is always a multiple of three (5.2 x 10^4 becomes 52 x 10^3), aligning with the SI prefixes (kilo, mega, giga, milli, micro, nano) used in physics and engineering. This calculator outputs all three forms simultaneously so you can choose whichever your context requires.
Arithmetic in exponential notation
Multiplication and division are especially clean in scientific notation. To multiply, multiply the coefficients and add the exponents: (3 x 10^4) x (2 x 10^3) = 6 x 10^7. To divide, divide the coefficients and subtract the exponents: (6 x 10^7) / (2 x 10^3) = 3 x 10^4. Addition and subtraction require equal exponents first: align the smaller number to match the larger exponent, then add or subtract the coefficients. Switch this calculator to Arithmetic mode to have all of that handled automatically for two operands at once.
Significant figures and precision
Significant figures (sig figs) tell you how precisely a measurement is known. The coefficient in scientific notation directly shows the sig-fig count: 5.20 x 10^4 has three sig figs (the trailing zero matters), while 5.2 x 10^4 has two. When multiplying or dividing, the result should have as many sig figs as the least-precise operand. When adding or subtracting, the result is limited by the least-precise decimal place. Use the significant-figures selector in this calculator to control how many digits appear in the coefficient.
SI prefixes and their engineering exponents
| Prefix | Symbol | Exponent | Value (decimal) |
|---|---|---|---|
| yotta | Y | 10^24 | 1,000,000,000,000,000,000,000,000 |
| zetta | Z | 10^21 | 1,000,000,000,000,000,000,000 |
| exa | E | 10^18 | 1,000,000,000,000,000,000 |
| peta | P | 10^15 | 1,000,000,000,000,000 |
| tera | T | 10^12 | 1,000,000,000,000 |
| giga | G | 10^9 | 1,000,000,000 |
| mega | M | 10^6 | 1,000,000 |
| kilo | k | 10^3 | 1,000 |
| (none) | - | 10^0 | 1 |
| milli | m | 10^-3 | 0.001 |
| micro | u | 10^-6 | 0.000001 |
| nano | n | 10^-9 | 0.000000001 |
| pico | p | 10^-12 | 0.000000000001 |
| femto | f | 10^-15 | 0.000000000000001 |
| atto | a | 10^-18 | 0.000000000000000001 |
| zepto | z | 10^-21 | 0.000000000000000000001 |
| yocto | y | 10^-24 | 0.000000000000000000000001 |
The 20 named SI prefixes, from yotta (10^24) to yocto (10^-24).
Frequently asked questions
What is the difference between scientific and exponential notation?
Exponential notation is the broad term for writing numbers as a base raised to a power. Scientific notation is a specific form of exponential notation that uses base 10 and requires the coefficient to be at least 1 but less than 10. All scientific notation is exponential notation, but exponential notation can use any base (2, e, 10, etc.). In everyday science and this calculator, the two terms are often used interchangeably because base-10 is assumed.
How do I convert a decimal to scientific notation by hand?
Move the decimal point until you have a single non-zero digit to its left. Count how many places you moved: right-moves give a negative exponent, left-moves give a positive one. For 0.00023, you move the decimal four places right to get 2.3, so the result is 2.3 x 10^-4. For 45,000, you move four places left to get 4.5, giving 4.5 x 10^4.
How do I multiply numbers in scientific notation?
Multiply the coefficients together, then add the exponents. If the result's coefficient is not between 1 and 10, adjust: for example, (4 x 10^3) x (5 x 10^2) = 20 x 10^5 = 2 x 10^6. Use this calculator's Arithmetic mode to handle this automatically.
What is E notation and when should I use it?
E notation replaces "x 10^" with the letter E: 5.2E4 means 5.2 x 10^4. It is used in spreadsheets, calculators, programming languages (Python, JavaScript, C), and scientific databases because it can be typed on a standard keyboard without special symbols. Use it whenever you need to paste an exponential value into a formula or code.
What is engineering notation and how is it different from scientific notation?
In engineering notation, the exponent is always a multiple of three (0, 3, 6, 9, -3, -6, etc.), which keeps numbers aligned with the SI prefix system. A value that would be 52 x 10^3 in engineering notation maps to the kilo prefix (k), so it can be written as 52 k. This is convenient when working with electrical components, data storage, or physical measurements where prefix labels are standard.
Can this calculator handle negative numbers?
Yes. Enter a negative number such as -0.0045 and the calculator converts it to -4.5 x 10^-3 in scientific notation, -4.5E-3 in E notation, and -4.5 x 10^-3 in engineering notation. The sign is carried through all arithmetic operations as well.
What are significant figures and how do I choose the right count?
Significant figures are the meaningful digits in a measurement. Choose sig figs based on the precision of your source data. If a measurement was made to three decimal places, use three sig figs. In calculations, the result is limited by the least-precise input: multiplied/divided results keep the fewest sig figs of either operand; added/subtracted results keep the fewest decimal places.