Fundamentals of pharmaceutical calculations

1. Fundamentals of pharmaceutical calculations Lecturer: dr. Asmaa abdelaziz Mohamed Faculty of pharamcay Ibn hayan University 1

2. Arabic Numbers Arabic numbers (such as 1, 2, 3, etc.) are used universally to indicate quantities. These numbers are easy to read and less likely to be confused. 2

3. Roman Numbers Roman numbers are used with the apothecary's system to designate quantities on prescription. In the Roman system, letters of the alphabet are used to designate numbers. A few commonly used Roman numerals and their Arabic equivalents are given in the following Table: 3

4. Fractions *A fraction is a portion of a whole number. *Fractions contain two numbers: the bottom number (referred to as denominator) and the top number (referred to as numerator). Examples: 1/2, 3/7, 6/7 etc 4

5. Decimals *Decimals are another means of expressing a fractional amount. A decimal is a fraction whose denominator is 10 or a multiple of 10. *Example: 0.8 = 8/10, 0.08 = 8/100, 0.008 = 8/1000 To convert fraction to decimal, divide the numerator by the denominator. *Example: 1/2 = 1 ÷ 2 = 0.5 Adding zeros to a decimal without changing the place of the numbers does not affect the value of the number. *Example: 0.4, 0.40, or 0.400; all these represent four-tenths 5

6. Percentage The word percent means parts per 100 parts and is represented by the symbol %. Therefore, 1% is the same as the fraction 1/100. Example: 5% = 5/100 To express a percent as a decimal, the percent is divided by 100 Example: 5% = 5 ÷ 100 = 0.05 To change a fraction to a percent, first change the fraction to a decimal and then multiply it by 100. If the number is already presented as a decimal, directly multiply by 100. Example: 1/25 = 0.04 x 100 = 4% In general, the percent can be calculated by the following law: • 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 = 𝑝𝑎𝑟𝑡 /𝑡𝑜𝑡𝑎𝑙∗100 6

7. Ratio A ratio is a general name indicates a relation of two numbers. It can be expressed as a fraction, decimal or percentage. Examples: Fraction 1/4 = 1 in relation to 4 = quarter. Decimal 0.25 = 25/100 = 25 in relation to 100= quarter. Percentage 25%= 25/100 = 25 in relation to 100= quarter. Ratios having the same values are equivalent (or proportional). Cross products of two equivalent ratios are equal, i.e., the product of the numerator of one and the denominator of the other always equals the product of the denominator of one and the numerator of the other. Example: 4/5 = 12/15 and the cross products of these equivalent ratios are equal, i.e., 4 x 15 = 5 x 12 = 60 Proportion 7

8. Proportion *Proportion Two equal fractions can be written as a proportion. Thus, a proportion is a statement of equality between two fractions. The following form may be used to express the proportion: 𝑎/ 𝑏 = 𝑐/ 𝑑 *Examples of equal fractions written as proportions: 12/15 = 4/5 *If one of the terms in a proportion is unknown, it can be designated as X. The value of "X" can be calculated by setting up a proportion and solving for the unknown X, as follows: • Find the product of cross multiplication of the numbers. • Simplify the equation to find the value of X 8

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10. Thank you