Scientific Notation Converter
Instantly convert any number to scientific notation, e notation, engineering notation, standard form, and real number. Supports very large, very small, and decimal values.
Notation Equivalents Reference Table
The notation equivalents reference table below shows how common numbers appear across all four notation formats for quick comparison.
| Standard Number | Scientific Notation | E Notation | Engineering Notation |
|---|---|---|---|
| 357,096 | 3.57096 x 105 | 3.57096e5 | 357.096 x 103 |
| 124.7 | 1.247 x 102 | 1.247e2 | 124.7 x 100 |
| 0.005600 | 5.600 x 10-3 | 5.600e-3 | 5.600 x 10-3 |
| 0.00098 | 9.8 x 10-4 | 9.8e-4 | 980 x 10-6 |
| 1,000,000 | 1 x 106 | 1e6 | 1 x 106 |
| 0.001 | 1 x 10-3 | 1e-3 | 1 x 10-3 |
What Is Scientific Notation?
Scientific notation is a method for expressing numbers as a value between 1 and 10 multiplied by a power of 10. It is written in the form a x 10b, where 1 ≤ |a| < 10. This format is widely used in science, engineering, and mathematics to handle very large or very small numbers cleanly and precisely.
For example, the speed of light (299,792,458 m/s) is expressed in scientific notation as 2.99792458 x 108 m/s.
How to Convert a Number to Scientific Notation
Converting to scientific notation follows a clear four-step process that works for any real number.
Step by Step Conversion Method
- Move the decimal point until exactly one non-zero digit sits to the left. The resulting decimal is the coefficient a.
- Count the number of places you moved the decimal point. That count is the exponent b.
- If you moved the decimal to the left, b is positive. If you moved right, b is negative. If no move was needed, b = 0.
- Write the result as a x 10b.
Example: Convert 357,096 to Scientific Notation
Move the decimal 5 places to the left to get 3.57096. Since you moved left, the exponent is positive 5. The result is 3.57096 x 105.
Example: Convert 0.005600 to Scientific Notation
Move the decimal 3 places to the right and remove leading zeros to get 5.600. Since you moved right, the exponent is negative 3. The result is 5.600 x 10-3. The trailing zeros are kept because they indicate significant figures.
Scientific Notation vs E Notation vs Engineering Notation
Scientific notation, e notation, and engineering notation all express numbers using powers of 10 but differ in formatting convention.
Scientific notation uses the format a x 10b where 1 ≤ |a| < 10. E notation replaces “x 10b” with the letter “e”, producing formats like 3.45e5, which is common in calculators and programming languages. Engineering notation restricts the exponent to multiples of 3 (0, 3, 6, 9…) so that prefixes like kilo, mega, and giga align naturally with the value.
Order of Magnitude Explained
Order of magnitude is the power of 10 in a number written in scientific notation. For 3.45 x 105, the order of magnitude is 5. It gives a quick way to compare the relative size of numbers. A number with order of magnitude 6 is roughly 10 times larger than one with order of magnitude 5.