How to use the scientific notation converter
- Type a number in any form: 123456, 0.000045, 1.5e8, or 3.2 x 10^-4. Commas are ignored.
- Optionally enter the number of significant figures to round to, from 1 to 40. Leave it blank to keep every digit you typed.
- Read the scientific notation, E notation, engineering notation and the standard decimal form.
- Use the significant figures line to see how many significant digits your typed number has under the usual counting rules.
Formula
Scientific notation: a x 10^n, with 1 <= |a| < 10 and n a whole number
E notation: aEn (for example 6.02E23)
Engineering notation: a x 10^n with n a multiple of 3 and 1 <= |a| < 1000
Rounding to k significant figures keeps the first k digits and rounds half up on the next digit
The converter works on the digits of the number as text, not as floating-point values. That keeps every digit exact and allows enormous or tiny exponents. Trailing zeros in a whole number without a decimal point, such as 1500, are treated as not significant because they are ambiguous.
Worked example
602,214,076,000,000,000,000,000 becomes 6.02214076 x 10^23, which is 6.02214076E23 in E notation and 602.214076 x 10^21 in engineering notation.
0.00045 becomes 4.5 x 10^-4. 1.5e8 expands to 150,000,000, and 3.2 x 10^-4 expands to 0.00032. The number 12,345 is 1.2345 x 10^4 in scientific notation and 12.345 x 10^3 in engineering notation.
Rounding to 3 significant figures turns 12345.6789 into 1.23 x 10^4, and 999.96 into 1.00 x 10^3, where the rounding carries into the next power of ten.
Moving the decimal point
To write a large number in scientific notation, move the decimal point left until one nonzero digit remains to its left, and count the moves as a positive exponent. For a small number, move the decimal point right and use a negative exponent. Reading it back, a positive exponent means move the point right and a negative exponent means move it left. Scientific notation makes very large and small quantities, such as the size of atoms or the distance to stars, easier to compare and calculate.
Which notation to use
Each form has a typical home.
- Scientific notation is standard in math and science classes.
- E notation is common in calculators, spreadsheets and programming languages.
- Engineering notation lines up with unit prefixes such as kilo, mega and milli, since its exponents are multiples of 3.
- Standard form is easiest to read for ordinary-sized numbers.
Significant figures
Significant figures count the digits that carry information about precision. Leading zeros never count, and trailing zeros count only when there is a decimal point or an exponent, as in 1500. or 1.50e3. When you ask for a number of significant figures, zeros are added if needed to show the requested precision. For general rounding to decimal places, use the rounding calculator, and for expression math the scientific calculator.
Assumptions and limits
- Input may use E notation or the "x 10^" form, with optional commas and a sign. Other formats are rejected with a message.
- Inputs longer than 200 characters or with exponents beyond 100,000 are refused.
- The standard decimal form is written out only when it is 400 digits or shorter.
- Rounding to significant figures uses half-up rounding on the exact digits.
- Everything runs in your browser. Nothing you enter is sent anywhere.
Frequently asked questions
How do you convert a number to scientific notation?
Move the decimal point until there is one nonzero digit to its left, and write the number of places moved as a power of 10. For 0.00045 the point moves four places right, giving 4.5 x 10^-4.
What is E notation?
It is a compact text form of scientific notation, where E stands for times ten to the power. 6.02E23 means 6.02 x 10^23. Calculators and spreadsheets use it because it avoids superscripts.
What is engineering notation?
It is scientific notation with the exponent forced to a multiple of 3, so the mantissa runs from 1 up to 999. 12,345 is 12.345 x 10^3, which matches the kilo prefix.
How many significant figures does 1500 have?
Without a decimal point it is ambiguous. This tool counts it as 2, treating the trailing zeros as padding. Writing 1500. or 1.500e3 shows that all four digits are significant.
Does the converter lose precision with huge numbers?
No. It treats the digits as text and does exact digit arithmetic, so even a number with hundreds of digits converts without rounding unless you ask for significant figures.