Scientific Notation Calculator
Convert one number, such as 0.000123 or 1.2e-4, to scientific, standard decimal and engineering notation as you type. It does no arithmetic. How it works
Use the Scientific Notation Calculator
About the Scientific Notation Calculator
0.000123 is 1.2300 × 10^-4 in scientific notation, 123.000 × 10^-6 in engineering notation and 0.000123 as a standard decimal. This scientific notation calculator reads one number, written plainly, with an exponent such as 1.2e-4 or as 4.5 × 10^-4, and shows the three forms as you type: scientific with 4 decimals, engineering with 3 and the standard decimal written out in full. Set significant figures from 1 to 17 to round: 123456 at 3 is 1.23 × 10^5.
Numbers in three notations
| Number typed | Scientific | Engineering | Standard decimal |
|---|---|---|---|
| 0.000123 | 1.2300 × 10^-4 | 123.000 × 10^-6 | 0.000123 |
| 0.005 | 5.0000 × 10^-3 | 5.000 × 10^-3 | 0.005 |
| 1.2e-4 | 1.2000 × 10^-4 | 120.000 × 10^-6 | 0.00012 |
| -350 | -3.5000 × 10^2 | -350.000 × 10^0 | -350 |
| 299792458 | 2.9979 × 10^8 | 299.792 × 10^6 | 299792458 |
| 6.022e23 | 6.0220 × 10^23 | 602.200 × 10^21 | 602200000000000000000000 |
| 12345.6789 | 1.2346 × 10^4 | 12.346 × 10^3 | 12345.6789 |
| 999.9999 | 1.0000 × 10^3 | 1.000 × 10^3 | 999.9999 |
| 1e-9 | 1.0000 × 10^-9 | 1.000 × 10^-9 | 0.000000001 |
Each row as the page shows it for that typed number.
How to use this tool
- Type a number in the Number field, as plain digits (0.005, -350), with an exponent (1.2e-4) or as a × 10^b (4.5 x 10^-4).
- Read the three forms under it. They update as you type, and there is no Convert button.
- To round, type a number of significant figures from 1 to 17. The scientific form and the decimal follow it, and the exact value is shown beside them.
Frequently asked questions
- How do you convert a number to scientific notation?
- Move the decimal point until one non-zero digit is left of it, then multiply by 10 raised to the number of places you moved: positive if you moved left, negative if you moved right. 299792458 becomes 2.9979 × 10^8 (8 places left) and 0.005 becomes 5.0000 × 10^-3 (3 places right). The calculator shows 4 decimals, so 2.99792458 is rounded to 2.9979.
- What is the difference between scientific and engineering notation?
- Scientific notation keeps the mantissa from 1 up to, but not including, 10. Engineering notation keeps the exponent a multiple of 3 and the mantissa from 1 to 999.999, so it lines up with metric prefixes. 12345.6789 is 1.2346 × 10^4 in scientific notation and 12.346 × 10^3 in engineering notation, and 0.000123 is 1.2300 × 10^-4 against 123.000 × 10^-6, which reads as 123 micro.
- How do I convert scientific notation to a normal number?
- Type it as written, such as 4.5 × 10^-4 (× can also be x, X or *), and read the standard decimal: 0.00045. E notation works too: 1.2e-4 means 1.2 × 10^-4 and gives 0.00012. 6.022e23 gives 6.0220 × 10^23 in scientific notation and 602200000000000000000000 as a standard decimal. A capital E, as calculators and spreadsheets print it (1E5), works too. Commas are refused, so 1,234 has to be typed as 1234.
- What are the largest and smallest numbers it can show?
- Above about 1.8 × 10^308, or below about 5 × 10^-324 (other than 0), the field shows a message, because a browser cannot store those values. The smallest number, 5e-324, shows as 4.9407 × 10^-324 in scientific notation and 4.941 × 10^-324 in engineering notation. About 15 to 17 significant digits of any number are exact and no more.
- Why does 999.9999 show as 1.0000 × 10^3?
- The mantissa is rounded to 4 decimals for scientific notation, and 9.999999 rounds up to 10.0000, so the exponent goes up to 3 to keep the mantissa below 10. Engineering notation does the same and shows 1.000 × 10^3. The standard decimal still reads 999.9999.
- How do I write a number in scientific notation to 3 significant figures?
- Type 3 in Significant figures. 123456 becomes 1.23 × 10^5 and the standard decimal 123000, with the exact value 123456 beside it. 299792458 at 3 figures is 3.00 × 10^8: the zeros stay, because they are significant. Engineering notation keeps its 3 decimals.
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