Scientific notation is a way to write real numbers that is very useful for very large and very small numbers. It is also useful in communicating the number of significant digits of a quantity and its order of magnitude. A number expressed in scientific notation is in the form a × 10^{b} were a is the mantissa or significand and b is the exponent. Example: 1.7×10^{3} = 1700.
In many computer languages numbers are written in E notation. E notation is in the form aE±b where aE+b = a × 10^{b} and aE-b = a × 10^{-b}. Example: 2.3E-02 = 2.3×10^{-2} = 0.023.
Another notation similar to scientific notation is engineering notation. Engineering notation is the same as scientific notation except that the exponent is always a multiple of three, and the mantissa is between -999.9 and 999.9. Example: 23.56×10^{3} = 23560.
More examples of numbers in these notations are:
Decimal format | Scientific notation | E notation | Engineering notation | Implied significant digits | Order of magnitude |
---|---|---|---|---|---|
1575000000 | 1.575 × 10^{5} | 1.575 E+05 | 157.5 × 10^{3} | 4 | 5 |
0.000000474 | 4.74 × 10^{-7} | 4.74 E -7 | 474 × 10^{-9} | 3 | -7 |
-4726.4 | -4.7264 × 10^{3} | -4.7264 E 3 | -4.7264 × 10^{3} | 5 | 3 |
Table 1: Examples of scientific, E and engineering notation |
Since a number expressed in scientific notation is a real number, all the properties and operations on real numbers apply. Numbers is scientific notation can be added, subtracted, multiplied and divided.
To subtract two numbers in scientific notation, add the first number (minuend) to the additive inverse (negative) of the second number (subtrahend).
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E | F | G | H | I |
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