Astronomy Answers: From the Astronomical Dictionary

Astronomy Answers
From the Astronomical Dictionary

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the exponential notation

Exponential notation is a method for writing numbers that is used a lot in science because it is convenient for writing the very large and very small numbers that occur often in science. Exponential notation consists of two numbers, the mantissa and the exponent. The mantissa is a number that may be fractional (with a part after the decimal point) and that is usually between 1 and 10. The exponent is a whole number that indicates by which power of 10 you should multiply the mantissa, so by how many places you should shift the decimal point to the left (if the exponent is negative) or the right (if the exponent is positive).

There are different methods in use for linking the mantissa and exponent of a number. The proper mathematical way is to put "times ten to the power of" between the mantissa and the exponent, but this requires the exponent to be written in superscript, a bit higher than normal, and that cannot be displayed properly (or at all) on simple screens. That's why in computer-related texts people usually put a letter "E" or "e" between the mantissa and the exponent.

For example, three million million million, a three followed by 18 zeros, is written in exponential notation as 3×1018 (the 18 ought to be written a bit higher than the 10, if your screen supports this) or 3 × 1018. So, 3.2 × 103 is equal to 3200 and 3.2 × 10−3 is equal to 0.0032.

In general, people use either exponential or normal notation, whichever is shorter. Exponential notation is convenient for describing numbers that are many orders of magnitude different from 1.