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# scientific notation

scientific notation, means of expressing very large or very small numbers in a compact form that is easy to use in computations. In this notation, any number is expressed as a number between 1 and 10 multiplied by a power of 10 that indicates the correct position of the decimal point in the original number; numbers greater than 10 are expressed by positive powers of 10 and numbers less than 1 are expressed by negative powers of 10 (see exponent). For example, 43,700 is written in scientific notation as 4.37 × 104 and 0.00526 as 5.26 × 10 - 3. The larger the converted number, the more compactness is achieved: for example, the speed of light, about 30,000,000,000 cm per sec, becomes 3 × 1010 cm per sec. Calculations are greatly simplified by use of scientific notation: the first parts of a pair of numbers to be multiplied or divided are combined manually or by slide rule and the powers of 10 are added or subtracted in accordance with the rules for exponents. If the first part of the result is greater than 10, an adjustment is made. For example, in order to multiply 832,000 by 0.00035, one converts first to scientific notation as follows: (832,000)×(0.00035) = (8.32×105)×(3.5×10 - 4) = 8.32×3.5×105×10 - 4 = 29.12×101 = 2.912×102 (in scientific notation) or 291.2 (in ordinary notation).

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