SigFig-ExpNotation

# SigFig-ExpNotation - E XPONENTIAL or SCIENTIFIC NOTATION...

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EXPONENTIAL or SCIENTIFIC NOTATION SigFig-Exp.wpd I. Exponential or scientific notation allows for the convenient expression of large and small numbers. These numbers are expressed as the product of a digit term and exponential term (power of 10). A. The speed of light in a vacuum is: 29,980,000,000 cm/s = 2.998 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 cm/s 2.998 x 10 cm/s 10 Digit Exponential Term B. The diameter of one Au atom is: 0.0000000358 cm = 3.58 x 1 cm 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 1 cm = 3.58 x 10 cm -8 10 8 II. Exponential notation may be adjusted without changing the value of the expression as long as the change in the digit term is matched in the opposite direction by the change in the exponential term. C Digit term increase (shift decimal placement to the right) requires. .. Exponential term decrease (becomes more negative) C Digit term decrease (shift decimal placement to the left) requires. .. Exponential term increase (becomes more positive) C Standard or conventional notation expresses the digit term between 1 and 10. 2.998 x = 29.98 x 10 0.2998 9 11 Standard 3.58 x 10 = 35.8 0.358 -8 -9 -7

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2 III. MATHEMATICAL OPERATIONS WITH EXPONENTIAL NOTATION A. Addition / Subtraction Exponential terms must be identical before digit terms are added , for example: (1.27 x 10 ) + (4 = ? 31 1.27 x 10 127 x 10 0.04 x 10 or 4 1.31 x 10 131 (3.2 x 10 ) - (5 10 ) = ? -4 -5 3.2 x 32 x 10 -4 -5 - 0.5 or - 5 -4 -5 2.7 27 -4 -5 B. Multiplication Multiply digit terms and add exponents , for example (A x 10 ) (B x 10 ) = AB x m n m+n (3 10 ) (2 ) = 3 2 = 6 2 18 2+18 20 (2 10 ) (4 10 ) = = 8 10 -6 4 -6+4 -2 (8.2 ) (1.0 10 ) = 8.2 1.0 = 8.2 -15 -6 -15+(-6) -21 C. Division Divide digit terms and subtract exponent of denominator from the exponent of the numerator, for example A x 10 = A n n-m B x 10 B m = 8 x = 4 x 6 6-3 3 2 3 15 x 10 = = 5 -14 -14-3 -17 3 x 10 3 3 24 x 10 = 24 = -2 -2-(-7) 5 8 8 -7
3 SIGNIFICANT FIGURES I. KINDS OF NUMBERS A. Exact Numbers are the result of a count or a defined relationship. They are assumed to contain an infinite number of significant figures. For example . . . 26 He atoms 2 ± 2 H atoms per 1 molecule of H O exact 12 in = 1 ft Volume = 4 B r 3 3 1 liter = 1000 milliliters B = 3.1415927 . . .

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## This note was uploaded on 11/16/2011 for the course CHM 2045 taught by Professor Mitchell during the Fall '07 term at University of Florida.

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SigFig-ExpNotation - E XPONENTIAL or SCIENTIFIC NOTATION...

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