NUMBERS AND NUMERALS A number is a total quantity or amount,
whereas a numeral is a word, sign, or group of words and signs
representing a number.
Slide 3
ARABIC AND ROMAN NUMERALS Arabic Numerals Arabic numerals, such
a 1, 2, 3, etc., are used universally to indicate quantities. These
numerals, which are represented by a zero and nine digits. Roman
Numerals Roman numerals are used with the apothecarys system of
measurement to designate quantities on prescription.
Slide 4
I. ROMAN NUMERALS
Slide 5
Roman numerals To express quantities in the roman system, eight
letters of fixed values are used : LetterValue ss I1 V5 X10 L50
C100 D500 M1000
Slide 6
Roman numerals There are four basic principles for reading and
writing Roman numerals: 1. A letter repeats its value that many
times (XXX = 30, CC = 200, etc.). A letter can only be repeated
three times. 2. If one or more letters are placed after another
letter of greater value, add that amount. VI = 6 (5 + 1 = 6)LXX =
70 (50 + 10 + 10 = 70)MCC = 1200 (1000 + 100 + 100 = 1200)
Slide 7
Roman numerals 3. If a letter is placed before another letter
of greater value, subtract that amount. IV = 4 (5 1 = 4) XC = 90
(100 10 = 90)CM = 900 (1000 100 = 900)
Slide 8
Roman numerals Several rules apply for subtracting amounts from
Roman numerals: A. Only subtract powers of ten (I, X, or C, but not
V or L)For 95, do NOT write VC (100 5). DO write XCV (XC + V or 90
+ 5) B. Only subtract one number from another. For 13, do NOT write
IIXV (15 1 - 1). DO write XIII (X + I + I + I or 10 + 3) C. Do not
subtract a number from one that is more than 10 times greater (that
is, you can subtract 1 from 10 [IX] but not 1 from 20there is no
such number as IXX.)For 99, do NOT write IC (C I or 100 - 1). DO
write XCIX (XC + IX or 90 + 9)
Slide 9
Roman numerals 4. A bar placed on top of a letter or string of
letters increases the numeral's value by 1,000 times. (XV = 15, but
XV = 15,000)
Slide 10
Roman numerals Example 1. Write the following in Roman: a) 27
b) 1876 c) 126 d) 999
Slide 11
Roman numerals 2. Write the following in Arabic: a) MCMLIX b)
xlviii c) Lxxxiv d) lxxii
Slide 12
3. Perform the following operations and indicate your answer in
Arabicnumbers: a) XII + VII b) XXVI XII c) XXIV VI d) XIX IX
Slide 13
II. FRACTIONS
Slide 14
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). The denominator in
the fraction is the total number of parts into which the whole
number is divided. The numerator in the fraction is the number of
parts we have.
Slide 15
Fractions A proper fraction should always be less than 1, i.e.,
the numerator is smaller than the denominator. Examples: 5/8, 7/8,
3/8 A proper fraction such as 3/8 may be read as 3 of 8 parts or as
3 divided by 8.
Slide 16
Fractions An improper fraction has a numerator that is equal to
or greater than the denominator. It is therefore equal to or
greater than one. Examples: 2/2 = 1, 5/4, 6/5 To reduce the
improper fraction, divide the numerator by the denominator.
Fractions Simplifying the fraction: find the largest number
(referred to as greatest common divisor) that will divide evenly
into each term. Examples: 15/20 = 15 5/20 5 = 3/4 12/18 = 12 6/18 6
= 2/3 7/21 = 7 7/21 7 = 1/3
Slide 19
Fractions Adding fraction: To add fractions reduce them to
common denomination, add the numerators, and the sum over the
common denominator Example: 4/6 + 2/5 = 20/30 + 12/30 = 32/30
Slide 20
Fractions Some numbers are expressed as mixed numbers (a whole
number and a fraction). To change mixed numbers to improper
fractions, multiply the whole number by the denominator of the
fraction and then add the numerator. Examples: 10 58 = 85/8 3 56 =
23/6
Slide 21
Fractions Subtracting of Fractions To subtract one fraction
from another, reduce them to a common denomination, subtract, and
write the difference over the common denominator. Example 7/12 1/8
= 14/24 3/24 = 11/24
Slide 22
Fractions Multiplying fractions To multiply fractions, multiply
the numerators and write the product over the product of the
denominators. Example 2/3 x 4/5 = 8/15 2/5 x 1/2 = 2/10 = 1/5
Reduce your answer to lowest terms, when possible.
Slide 23
Fractions Dividing fraction: To divide a whole number or a
fraction by a proper or improper fraction, invert the divisor and
multiply. Example: 4/5 2/3 = 4/5 3/2 = 6/5 or 1 15
Slide 24
Fractions 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 A decimal mixed number is a whole number and a decimal
fraction. Example: 4.3 = 4 3/10
Slide 25
Fractions Example 1. A bottle of Childrens Tylenol contains 30
teaspoonfuls of liquid. If each dose is 12 teaspoonful, how many
doses are available in this bottle? 2. A prescription contains 3/5
gr of ingredient A, 2/4 gr of ingredient B, 6/20 gr of ingredient
C, and 4/15 gr of ingredient D. Calculate the total weight of the
four ingredients in the prescription?
Slide 26
Fractions 3. A pharmacist had 10 g of codeine sulfate. If he
used it in preparing 5 capsules each containing 0.025 g, 10
capsules each containing 0.010 g, and 12 capsules each containing
0.015 g, how many g of codeine sulfate were left after he prepared
all the capsules?
Slide 27
LOGARITHM
Slide 28
Logarithm The logarithm of a positive number N to a given base
b is the exponent x to which the base must be raised to equal the
number N. Therefore, if N = b x then log b N = x For example, with
common logarithms (log), or logarithms using base 10, 100 = 10 2
then log 100 = 2, The number 100 is considered the antilogarithm of
2.
Slide 29
CONVERSION OF TEMERATURE
Slide 30
Conversion of temerature Temperature is measured with a
thermometer. Standard Scales: Use the freezing and boiling points
of water at atmospheric pressure as basis. Fahrenheit o F (32 -
212) o F = (1.8 x o C) + 32 Celsius o C (0 -100) o C = ( o F -
32)/1.8
Slide 31
A thermometer on the wall of a room reads 86 F. What is the
room temperature in C.
Slide 32
Home work Write the following in Roman numerals: 1. 28 2. 65 3.
17 4. 1763 Convert the following Roman numerals to Arabic numerals:
1. xlvi 2. lxxiv 3. xlvii 4. xxxix A tablet contains 1/20 gr of
ingredient A, 1/4 gr of ingredient B, 1/12 gr of ingredient C, and
enough of ingredient D to make a total of 20 gr. How many grains of
ingredient D are in the tablet? Convert 140 C to F