By Michael C. Makoid, Ph.D., Phillip J. Vuchetich, Pharm.D., M.S., Umesh V. Banakar, Ph.D.

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**Example text**

Any number multiplied by infinity ( ∞ ) equals infinity. Any number divided by zero is mathematically undefined. Any number divided by infinity is mathematically undefined. 2 EXPRESSING LARGE AND SMALL NUMBERS Large or small numbers can be expressed in a more compact way using indices. How Does Scientific Notation Work? 08 ×10 In general a number takes the form: A × 10 n Where A is a value between 1 and 10, and n is a positive or negative integer The value of the integer n is the number of places that the decimal point must be moved to place it immediately to the right of the first non-zero digit.

85 Logarithms to the base 10 are known as Common Logarithms. The transformation of a number (A) to its logarithm (n) is usually made from tables, or on a scientific calculator; the reverse transformation of a logarithm to a number is made using anti-logarithmic tables, or on a calculator. What is the characteristic? the mantissa? 6 The number before the decimal point is called the characteristic and tells the placement of the decimal point (to the right if positive and to the left if negative).

Hence, y + dy = ( x + dx ) 3 (EQ 1-14) Multiplying out: 3 2 2 y + dy = x + 3x ( dx) + 3x ( dx ) + ( dx ) 3 (EQ 1-15) (c) The change in y is obtained by subtraction of the original expression from the last expression. , Eq. 2 - Eq. 1) 2 2 dy = 3x ( dx ) + 3x ( dx ) + ( dx ) 3 (EQ 1-16) Dividing throughout to obtain the derivative, 2 2 dy ------ = 3x + 3x ( dx ) + ( dx ) dx When dx is infinitesimally small, its magnitude tends to zero ( dx → 0 ) . The limiting value of this tendency must be dx = 0 .