Scientific Notation Calculator

Convert any number to scientific notation.

Number

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Scientific notation

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Mantissa (coefficient)—

Exponent—

How it works

Scientific notation, also called standard form, writes very large or very small numbers as a coefficient multiplied by a power of ten. It keeps otherwise unwieldy figures readable and makes their scale obvious at a glance, which is why it is the default in science and engineering. This scientific notation calculator converts any number you enter into the form mantissa times ten to an exponent, and it also breaks out the mantissa and exponent separately so you can use them in further work. The mantissa is a number whose magnitude sits between one and ten, and the exponent records how many places the decimal point moved to get there. A positive exponent means the original number was large, while a negative exponent means it was a small fraction. For example, 0.00042 becomes 4.2 times ten to the power of negative four, instantly revealing that the value has four leading zeros after the decimal point. Astronomers writing distances in kilometres, chemists counting molecules, and physicists handling atomic scales all lean on scientific notation to avoid long strings of zeros that are easy to miscount. This scientific notation calculator removes the manual place-counting and gives you a clean, unambiguous expression every time.

Formula

number = mantissa × 10^exponent, with exponent = ⌊log₁₀|number|⌋

Scientific notation rewrites a number as a coefficient between one and ten multiplied by a power of ten. The exponent is the floor of the base-ten logarithm of the number's absolute value, which counts how many places the decimal point must shift. Dividing the original number by ten raised to that exponent yields the mantissa, so the two parts multiply back exactly to the value you started with, only expressed compactly.

Source:Standard mathematics

We review all our tools from time to time to ensure accuracy.

Worked example

Number:0.00042

0.00042 = 4.2 × 10^-4, so the mantissa is 4.2 and the exponent is -4.

How to use this calculator

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Frequently asked questions

What is scientific notation used for?

Scientific notation compresses numbers that would otherwise carry long runs of zeros, making them easier to read, write, and compare. It is standard in physics, chemistry, astronomy, and engineering, where quantities range from atomic sizes to galactic distances. It also makes the order of magnitude explicit, so you can quickly see that one value is a thousand times larger than another simply by comparing their exponents rather than counting digits.

What is the mantissa?

The mantissa, also called the coefficient or significand, is the leading part of a number in scientific notation. Its magnitude always sits between one and ten, so there is exactly one non-zero digit before the decimal point. In 4.2 times ten to the negative four, the mantissa is 4.2. The mantissa carries the significant figures of the value, while the exponent records only the scale.

How does the exponent work?

The exponent is the power of ten that scales the mantissa back to the original number, and it equals the number of places the decimal point shifts. A positive exponent means you move the point to the right, producing a large number, while a negative exponent moves it left, producing a small fraction. So ten to the sixth means a million, and ten to the negative three means one thousandth.

How do I convert a small decimal?

Move the decimal point to the right until exactly one non-zero digit sits in front of it, counting the moves as you go. That count becomes a negative exponent because the original value was smaller than one. For 0.00042 you shift four places to reach 4.2, so the result is 4.2 times ten to the negative four. The calculator performs this shift automatically for any input.

What is scientific notation for zero?

Zero is a special case because it has no non-zero digits and no meaningful order of magnitude, so it cannot be written as a mantissa times a power of ten in the usual way. By convention the calculator simply reports zero as itself, with a mantissa and exponent of zero. Every other number, positive or negative, large or small, converts to a proper mantissa between one and ten.