Convert to and from scientific and engineering notation.
Very large and very small numbers are hard to read and easy to miscount. A scientific notation calculator writes them as a number between 1 and 10 multiplied by a power of 10, so 0.000045021 becomes 4.5021 × 10⁻⁵. It also gives E notation for calculators and spreadsheets, and engineering notation, and converts in the other direction too.
Quick answer: to write a number in scientific notation, move the decimal point until one non-zero digit is in front of it, then multiply by 10 to the power of the number of places moved. 4,500 = 4.5 × 10³ and 0.0045 = 4.5 × 10⁻³.
In the UK, scientific notation is often called standard form. They are the same thing.
How to Use the Scientific Notation Calculator
Number → notation
- Enter a number, such as 0.000045021 or 299792458. You can also type E notation, such as 6.02e23.
- Read the scientific notation, E notation, engineering notation and the full decimal.
Notation → number
- Enter the coefficient, such as 6.022, and the power of 10, such as 23.
- Read the number written out in full.
How Scientific Notation Works
A number in scientific notation has the form a × 10ⁿ, where:
- a is at least 1 and less than 10, and
- n is a whole number, positive for big numbers and negative for small ones.
To convert, move the decimal point until one non-zero digit is in front of it. Count the places you moved:
- Moved left (a big number): the exponent is positive.
- Moved right (a small number): the exponent is negative.
Scientific Notation Examples
299,792,458 (the speed of light in m/s). Move the point 8 places left: 2.99792458 × 10⁸.
0.000045021. Move the point 5 places right: 4.5021 × 10⁻⁵. In E notation, 4.5021e-5. In engineering notation, 45.021 × 10⁻⁶.
6.022 × 10²³ (Avogadro’s number, rounded to 4 significant figures). Move the point 23 places right: 602,200,000,000,000,000,000,000.
Scientific, E and Engineering Notation
| Format | 0.000045021 | When it is used |
|---|---|---|
| Scientific notation | 4.5021 × 10⁻⁵ | Maths and science |
| E notation | 4.5021e-5 | Calculators, spreadsheets and code |
| Engineering notation | 45.021 × 10⁻⁶ | Engineering. The exponent is always a multiple of 3, which matches unit prefixes such as micro (10⁻⁶) |
In engineering notation, 45.021 × 10⁻⁶ metres reads directly as 45.021 micrometres.
Powers of 10 and Unit Prefixes
| Prefix | Symbol | Power of 10 | Example |
|---|---|---|---|
| tera | T | 10¹² | 1 terabyte ≈ 10¹² bytes |
| giga | G | 10⁹ | 1 gigawatt = 10⁹ watts |
| mega | M | 10⁶ | 1 megajoule = 10⁶ joules |
| kilo | k | 10³ | 1 kilometre = 10³ metres |
| milli | m | 10⁻³ | 1 millimetre = 10⁻³ metres |
| micro | µ | 10⁻⁶ | 1 micrometre = 10⁻⁶ metres |
| nano | n | 10⁻⁹ | 1 nanosecond = 10⁻⁹ seconds |
| pico | p | 10⁻¹² | 1 picofarad = 10⁻¹² farads |
Calculating With Scientific Notation
- Multiplying: multiply the front numbers and add the powers. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷.
- Dividing: divide the front numbers and subtract the powers. (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴.
- Adding or subtracting: make the powers the same first. 3 × 10⁴ + 5 × 10³ = 3 × 10⁴ + 0.5 × 10⁴ = 3.5 × 10⁴.
The scientific calculator accepts numbers in this form through its EXP key.
Scientific Notation FAQs
What is standard form?
In the UK, standard form means scientific notation: a number from 1 up to (but not including) 10, multiplied by a power of 10. In some US classes, “standard form” means a number written out in full, so check which your teacher means.
How do I type scientific notation on a calculator?
Use the EXP or EE key, or type E. 6.022 × 10²³ is entered as 6.022E23.
Is 12 × 10⁴ in scientific notation?
No, because 12 is not between 1 and 10. Written correctly, it is 1.2 × 10⁵.
How do I round in scientific notation?
Round the front number to the number of significant figures you need. 4.5021 × 10⁻⁵ to 3 significant figures is 4.50 × 10⁻⁵. For rounding to decimal places instead, use the rounding calculator.
How we checked this page: each conversion was checked by counting decimal places by hand, and matches the calculator in all three formats.