<P> Any given real number can be written in the form m × 10 ^ in many ways: for example, 350 can be written as 7002350000000000000 ♠ 3.5 × 10 or 7002350000000000000 ♠ 35 × 10 or 7002350000000000000 ♠ 350 × 10 . </P> <P> 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 (1 ≤ m <10). Thus 350 is written as 7002350000000000000 ♠ 3.5 × 10 . This form allows easy comparison of numbers, as the exponent n gives the number's order of magnitude . In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as 6999500000000000000 ♠ 5 × 10). The 10 and exponent are often omitted when the exponent is 0 . </P> <P> Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized form, such as engineering notation, is desired . Normalized scientific notation is often called exponential notation--although the latter term is more general and also applies when m is not restricted to the range 1 to 10 (as in engineering notation for instance) and to bases other than 10 (for example, 3.15 × 2 ^). </P> <P> 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 . Though similar in concept, engineering notation is rarely called scientific notation . Engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication . For example, 6992125000000000000 ♠ 12.5 × 10 m can be read as "twelve - point - five nanometers" and written as 6992125000000000000 ♠ 12.5 nm, while its scientific notation equivalent 6992125000000000000 ♠ 1.25 × 10 m would likely be read out as "one - point - two - five times ten - to - the - negative - eight meters". </P>

What is the difference between exponential and scientific notation
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