- Exponential notation is an alternative method of expressing numbers.
- Exponential numbers take the form a
^{n}, where a is multiplied by itself n times.

A simple example is 8=2^{3}=2×2×2. - In exponential notation, a is termed the base while n is termed the power or exponent or index.
- Scientific notation is a specific example of exponential numbers, 10 is almost always used as the base number.

Thus 10^{3}means 10×10×10, while 10^{-3}is the notation for the reciprocal of 10^{3}namely 1/1000. - The other name for this mathematical format is
**standard form**( you may have come across this in GCSE mathematics). - Expressing numbers which are not whole powers of 10 in scientific notation often requires a further multiplier, termed the
**coefficient**(C), giving the expression in the form C ×10^{n}.

For example, 5 ×10^{3}is the scientific notation for the number 5000, while 3.25×10^{2}is the scientific notation for the number 325.

Similarly, 3.25×10^{-2}would represent3.25 × 1 100= 3.25 100=0.0325. -
**Convention**

It is scientific convention to express all such numbers as coefficients between 1 and 10 and followed by an appropriate power of 10.**Examples**35200 = 3.52 ×10 ^{4}NOT 352 ×10^{2}NOT 35.2 ×10^{3}1750 = 1.75 ×10 ^{3}NOT 175 ×10 NOT 17.5 ×10^{2}0.0436 = 4.36 ×10 ^{-2}NOT 0.436 ×10^{-1}NOT 43.6 ×10^{-3} - You should use such scientific notation whenever you express very large or very small numbers - it is a recognized form of "shorthand", and it avoids spurious accuracy e.g. writing 9 000 000 suggests that the number is exactly 9 million, in contrast to 9.0 ×10
^{6}which suggests no such accuracy beyond the first decimal place of the coefficient.

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On 04 Aug 2008, 19:35.