Scientific notation

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Scientific notation, also known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is often favored by scientists, mathematicians, doctors, and engineers, who work with such numbers.

In scientific notation all numbers are written like this:

("a times ten to the power of b"), where the exponent b is an integer, and the coefficient a is any real number (but see normalized notation below), called the significand or mantissa (though the term "mantissa" may cause confusion as it can also refer to the fractional part of the common logarithm). If the number is negative then a minus sign precedes a (as in ordinary decimal notation).

Contents

Normalized notation

Any given number can be written in the form of a×10^b in many ways; for example 350 can be written as 3.5×102
or 35×101
or 350×100
.

In normalized scientific notation, the exponent b is chosen such that the absolute value of a remains at least one but less than ten (1 ≤ |a| < 10). For example, 350 is written as 3.5×102
. This form allows easy comparison of two numbers of the same sign in a, as the exponent b gives the number's order of magnitude. In normalized notation the exponent b is negative for a number with absolute value between 0 and 1 (e.g., minus one half is −5×10−1
). The 10 and exponent are usually omitted when the exponent is 0. Note that 0 itself cannot be written in normalised scientific notation since the mantissa would have to be zero and the exponent undefined.

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