Scientific Notation Converter
Write any number in scientific, E, engineering and SI-prefix form. Round to significant figures, or multiply, divide, add and subtract numbers in scientific notation, exactly.
How to Use
- Choose Convert to rewrite one number, or Calculate to multiply, divide, add or subtract two.
- Type a number in any form: 299792458, 6.02e23, 4.7 × 10^-6, or with an SI prefix such as 4.7k or 47µ.
- Optionally enter how many significant figures to round to.
- Read the scientific, E-notation, engineering and SI-prefix forms; the ruler shows where the number sits among the powers of ten.
- Show Work explains how far the point moved and why.
Worked Example
The speed of light, 299,792,458 m/s. Move the point left until one digit is in front of it: 8 places, so it is 2.99792458 × 10⁸, written 2.99792458e+8 on a calculator. For engineering form the power must be a multiple of 3, so use 10⁶ and move the point back two places: 299.792458 × 10⁶, which is 299.792458 mega. To 4 significant figures it is 2.998 × 10⁸.
Multiplying: (3 × 10⁸) × (2 × 10⁻³). Multiply the front numbers, 3 × 2 = 6, and add the powers, 8 + (−3) = 5: 6 × 10⁵, or 600,000.
The common mistake: the sign of the power. Small numbers have negative powers. 0.000047 is 4.7 × 10⁻⁵, because the point moves 5 places to the right to get 4.7; writing 4.7 × 10⁵ makes it 470,000, ten billion times too big.
Show Work
Formulas
Counting Sand and Stars
Writing huge numbers by their powers is ancient. In The Sand Reckoner Archimedes invented a system of orders and periods to show that the grains of sand needed to fill the universe, as he pictured it, came to about 10⁶³. Powers-of-ten notation in its modern form spread with logarithms in the 17th century, and the E of calculators and computers comes from FORTRAN in the 1950s, which wrote 6.02 × 10²³ as 6.02E23 because punch cards had no superscripts.
The SI prefixes give each third power a name. Kilo, mega and milli date from the metric system of the 1790s; giga and tera were added in 1960, and in 2022 the General Conference on Weights and Measures added ronna, quetta, ronto and quecto for 10²⁷, 10³⁰, 10⁻²⁷ and 10⁻³⁰, mainly for the size of the world’s data.
About This Calculator
This tool writes any number in scientific notation, E notation, engineering notation and with an SI prefix, rounds it to the significant figures you choose, counts the significant figures you typed, and multiplies, divides, adds or subtracts numbers in scientific notation. It reads plain decimals, E notation, “× 10^n” and prefixed values such as 4.7k, and it calculates exactly, so 0.1 × 3 is 0.3.
Everything runs in your browser; nothing is sent anywhere. The ruler marks where the number falls among the powers of ten, with the SI prefix at every third power.
Related calculators: Scientific Calculator, IEEE 754 Float Converter, and Number Base Converter.
Frequently Asked Questions
How do you write a number in scientific notation?
Move the decimal point until exactly one non-zero digit is in front of it, and count the moves. Moving left gives a positive power of ten, moving right a negative one. 299,792,458 needs 8 moves left: 2.99792458 × 10⁸. 0.000047 needs 5 moves right: 4.7 × 10⁻⁵.
What is engineering notation?
Scientific notation with the power of ten restricted to multiples of 3, so the number in front is between 1 and 999. That matches the SI prefixes: 4.7 × 10⁻⁵ becomes 47 × 10⁻⁶, which is 47 micro, the way you would read a 47 µF capacitor.
What does 6.02e23 mean?
It is E notation, the way calculators and programming languages write scientific notation: e23 means × 10²³. So 6.02e23 is 6.02 × 10²³, and 1.5e-9 is 1.5 × 10⁻⁹. It has nothing to do with the number e = 2.718.
How do I multiply and divide in scientific notation?
Multiply or divide the front numbers and add or subtract the powers. (3 × 10⁸) × (2 × 10⁻³) = 6 × 10⁵; (6.0 × 10²³) ÷ (2.0 × 10³) = 3.0 × 10²⁰. If the front number ends up 10 or more, move the point once more and add 1 to the power.
How many significant figures does a number have?
Count from the first non-zero digit. Zeros after the point at the end count, because someone measured them: 0.004560 has 4. Zeros at the end of a whole number are ambiguous: 1200 might have 2, 3 or 4, which is exactly what scientific notation fixes: 1.20 × 10³ has 3.
How do I use the Scientific Notation Converter?
Simply type or paste your value and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Physics
The speed of light, 299,792,458 m/s, is 2.998 × 10⁸ to 4 significant figures.
Chemistry
Avogadro’s number, 6.02214076 × 10²³, is 602.214076 × 10²¹, or about 602 zetta.
Electronics
0.000047 F is 4.7 × 10⁻⁵ F, or 47 µF in engineering form.
Homework
(3 × 10⁸) × (2 × 10⁻³) = 6 × 10⁵, with the powers added in the working.
Last updated: