🔬 Scientific Notation Calculator: Convert To and From Standard Form

What is the Scientific Notation Calculator?

Scientific notation writes a number as a coefficient multiplied by a power of ten, in the form a x 10^b, where the coefficient a is at least 1 but less than 10 and the exponent b is a whole number. The point of the format is to make very large and very small numbers readable: instead of writing 0.00000000066 you write 6.6 x 10^-10, and instead of 299,792,458 you write 2.99792458 x 10^8. The exponent tells you how many places the decimal point moves and in which direction, so it doubles as a quick measure of size.

Converting a plain decimal to scientific notation is a matter of sliding the decimal point until exactly one non-zero digit sits in front of it, then counting how far you moved. Moving the point to the left gives a positive exponent (the number was large); moving it to the right gives a negative exponent (the number was small). For 91,500 the point moves four places left, giving 9.15 x 10^4. For 0.00042 the point moves four places right, giving 4.2 x 10^-4. Going the other way, from scientific notation back to a decimal, you simply shift the point by the exponent and pad with zeros.

This tool also shows two close relatives of scientific notation. E-notation is the same idea written in a form computers and calculators understand, where x 10^b becomes the letter e followed by the exponent, so 4.2 x 10^-4 is typed as 4.2e-4. Engineering notation keeps the same value but forces the exponent to be a multiple of three, so it lines up with metric prefixes such as kilo (10^3), mega (10^6), milli (10^-3) and micro (10^-6); that is why an engineer writes 47,000 ohms as 47 x 10^3 rather than 4.7 x 10^4.

The number of significant figures you choose controls the precision of the coefficient, not the size of the number. Asking for three significant figures rounds 2.99792458 x 10^8 to 3.00 x 10^8, while ten significant figures keeps the full coefficient. Significant figures matter in science because they signal how precisely a quantity was measured, so the selector here lets you match the precision of your source data instead of inventing digits that were never measured.

When to use it

• Converting measurements in physics, chemistry and biology to and from standard form for lab reports and exams.
• Reading and entering very large or very small values such as Avogadro's number or the mass of an electron.
• Switching a value into engineering notation so it matches metric prefixes like kilo, mega, milli and micro.
• Rounding a coefficient to a set number of significant figures to match the precision of measured data.
• Checking homework answers that ask you to express a number in scientific or standard form.
• Comparing the order of magnitude of two numbers quickly by looking at their exponents.

How to use the Scientific Notation Calculator

1. Type a number in the input box, either as a plain decimal (0.00042 or 91500) or in E-notation (4.2e-4 or 9.15E4).
2. Pick how many significant figures you want the coefficient to keep using the selector (the default is 6).
3. Read the results: scientific notation, E-notation, engineering notation, standard decimal form and the order of magnitude.
4. Use the Copy button on any result to place that form on your clipboard, or click a sample chip to try a preset value.

Formula & method

Worked examples

Everyday numbers written in scientific notation

Exponents, metric prefixes and engineering notation

Common mistakes to avoid

• Leaving the coefficient outside the 1 to 10 range. In proper scientific notation the coefficient must be at least 1 and less than 10. Writing 42 x 10^-5 or 0.42 x 10^-3 has the right value but the wrong form; the correct version is 4.2 x 10^-4. Engineering notation is the one exception, where the coefficient can run up to 999.
• Getting the sign of the exponent backwards. A small number less than 1 has a negative exponent and a large number has a positive exponent. Moving the decimal point to the right (for a small number) gives a negative exponent; moving it to the left (for a large number) gives a positive one. 0.00042 is 4.2 x 10^-4, not 4.2 x 10^4.
• Confusing significant figures with decimal places. Significant figures count the meaningful digits in the coefficient, not the digits after the decimal point in the original number. Rounding 2.99792458 x 10^8 to three significant figures gives 3.00 x 10^8, regardless of how many zeros the standard form has.
• Forgetting that engineering exponents must be multiples of three. Engineering notation only uses exponents that are multiples of 3 so they map onto metric prefixes. 4.7 x 10^4 is valid scientific notation but not engineering notation; the engineering form is 47 x 10^3, which reads naturally as 47 kilo-units.

Glossary

Scientific notation

A way of writing a number as a coefficient times a power of ten, a x 10^b, with 1 <= |a| < 10.

Coefficient (mantissa)

The number a in a x 10^b, always at least 1 and less than 10 in standard scientific notation.

Exponent

The integer b in a x 10^b that says how many places the decimal point moves and in which direction.

E-notation

A computer-friendly form of scientific notation where x 10^b is written as the letter e followed by the exponent, such as 4.2e-4.

Engineering notation

Scientific notation in which the exponent is forced to a multiple of three so it matches metric prefixes like kilo and milli.

Order of magnitude

The exponent b of a number in scientific notation, used as a rough measure of its size.

Significant figures

The meaningful digits in a number that carry information about its precision; here they set the precision of the coefficient.

Frequently asked questions