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Lab 1

Lab 1. Prerequisite Mathematics Review. 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. ARABIC AND ROMAN NUMERALS Arabic Numerals

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Lab 1

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  1. Lab 1 Prerequisite Mathematics Review

  2. 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.

  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 apothecary’s system of measurement to designate quantities on prescription.

  4. I. Roman numerals

  5. Roman numerals • To express quantities in the roman system, eight letters of fixed values are used :

  6. Roman numerals • There are four basic principles for reading and writing Roman numerals: • A letter repeats its value that many times (XXX = 30, CC = 200, etc.). A letter can only be repeated three times. • 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)

  7. Roman numerals • 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)

  8. Roman numerals Several rules apply for subtracting amounts from Roman numerals: • 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) • 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) • 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 20—there 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)

  9. Roman numerals • A bar placed on top of a letter or string of letters increases the numeral's value by 1,000 times. (XV = 15, but X̅V̅ = 15,000)

  10. Roman numerals • Example • Write the following in Roman: • 27 • 1876 • 126 • 999

  11. Roman numerals • Write the following in Arabic: • MCMLIX • xlviii • Lxxxiv • lxxii

  12. Perform the following operations and indicate your answer in Arabicnumbers: • XII + VII • XXVI − XII • XXIV ÷ VI • XIX × IX

  13. II. Fractions

  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.

  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, 3/8A proper fraction such as 3/8 may be read as ‘‘3 of 8 parts’’ or as ‘‘3 divided by 8.’’

  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.

  17. Fractions • Examples:8/8 = 8 ÷ 8 = 16/4 = 6 ÷ 4 = 1 2⁄49/4 = 9 ÷ 4 = 2 1⁄4

  18. 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 = 3/412/18 = 12 ÷ 6/18 ÷ 6 = 2/3 7/21 = 7 ÷ 7/21 ÷ 7 = 1/3

  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

  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 5⁄8 = 85/83 5⁄6 = 23/6

  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. • Example7/12 – 1/8 = 14/24 – 3/24 = 11/24

  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 = 8/152/5 x 1/2 = 2/10 = 1/5Reduce your answer to lowest terms, when possible.

  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 1⁄5

  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 = 8/100.08 = 8/1000.008 = 8/1000 • A decimal mixed number is a whole number and a decimal fraction. • Example:4.3 = 4 3/10

  25. Fractions • Example • A bottle of Children’s Tylenol contains 30 teaspoonfuls of liquid. If each dose is 1⁄2 teaspoonful, how many doses are available in this bottle? • 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?

  26. Fractions • 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?

  27. Logarithm

  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 = bx then logb N = x • For example, with common logarithms (log), or logarithms using base 10,100 = 102 then log 100 = 2, The number 100 is considered the antilogarithm of 2.

  29. Conversion of temerature

  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 oF (32 - 212) oF = (1.8 xoC) + 32 • Celsius oC (0 -100) oC = (oF - 32)/1.8

  31. A thermometer on the wall of a room reads 86 Fº. What is the room temperature in Cº.

  32. Home work • Write the following in Roman numerals: • 28 • 65 • 17 • 1763 • Convert the following Roman numerals to Arabic numerals: • xlvi • lxxiv • xlvii • 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°

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