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6.49 x 102
(Scientific Notation)
6.49 x 10^2
(use the caret symbol [^] to type or write)
6.49E+2
(Scientific E-notation)
649
(Real Number)
Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators it is known as "SCI" display mode.
How to convert numbers or decimals to scientific notation?
In scientific notation all numbers are written in the form of m×10n
(m times ten raised to the power of n), where the exponent n is an integer, and the coefficient m is any real number, called the significand or mantissa. If the number is negative then a minus sign precedes m (as in ordinary decimal notation). See example below:
| Numbers | Scientific notation | e-notation |
|---|---|---|
| 3 | 3×100 | 3E+0 |
| 0.2 | 2×10-1 | 2E-1 |
| 500 | 5×102 | 5E+2 |
| 9,876.543 | 9.876543×103 | 9.876543E+3 |
| −24,000 | −2.4×104 | 2.4E+4 |
| 8,720,000,000 | 8.72×109 | 8.72E+9 |
| 0.00000000691 | 6.91×10-9 | 6.91E-9 |
In normalized scientific notation (called "standard form" in the UK), the exponent n is chosen so that the absolute value of m remains at least one but less than ten. Thus 350 is written as 3.5×102.
In Engineering notation (often named "ENG" display mode on scientific calculators) differs from normalized scientific notation in that the exponent n is restricted to multiples of 3. Consequently, the absolute value of m is in the range 1 ≤ |m| < 1000, rather than 1 ≤ |m| < 10. For example, 12.5×10-9 m can be read as "twelve-point-five nanometers" and written as 12.5 nm, while its scientific notation equivalent 1.25×10-8 m would likely be read out as "one-point-two-five times ten-to-the-negative-eight meters".
Scientific e-notation can be found on most calculators and many computer programs, they present very large and very small results in scientific notation, typically invoked by a key labelled EXP (for exponent), EEX (for enter exponent), EE, EX, E, or ×10x depending on vendor and model. In most programs, 6.022E23 (or 6.022e23) is equivalent to 6.022×1023, and 1.6×10-35 would be written 1.6E-35.
English format used in; Australia, Canada (English-speaking, unofficial), China, Hong Kong, Ireland, Israel, Japan, Korea, Malaysia, Mexico, New Zealand, Pakistan, Philippines, Singapore, Taiwan, Thailand, United Kingdom, United States.
French format used in; Albania, Austria, Belgium, Brazil, Bulgaria, Canada (French-speaking), Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Italy, Kosovo, Latin Europe, Netherlands, Norway, Peru, Poland, Portugal, Romania, Russia, Serbia, Slovakia, Slovenia, South Africa, Spain, Sweden, Switzerland (officially encouraged for non-currency numbers), Ukraine.
Spanish/Arabic format used in; Argentina, Austria, Bosnia and Herzegovina, Brazil, Chile, Croatia, Denmark, Germany, Greece, Indonesia, Italy, Netherlands (currency), Portugal, Romania, Russia, Slovenia, Spain, Sweden (not recommended), Turkey.