Medical Dosage Calculations

Transcription

1 Medical Dosage Calculations Ninth Edition Chapter 1 Review of Arithmetic for Medical Dosage Calculations Learning Outcomes 1. Convert decimal numbers to fractions. 2. Convert fractions to decimal numbers. 3. Round decimal numbers to a desired number of places. 4. Multiply and divide decimal numbers. 5. Multiply and divide fractions. 6. Simplify complex fractions. 7. Write percentages as decimal numbers. 8. Write percentages as fractions. Changing Decimal Numbers and Whole Numbers to Fractions 1

2 Changing Decimal Numbers to Fractions A decimal number represents a fraction with a denominator of 10, 100, 1000, and so on. Each decimal number has three parts: the whole number part, the decimal point, and the fraction part. Changing Decimal Numbers to Fractions Reading a decimal position will help you to write it as a fraction: Decimal Number Read Fraction 4.1 four and one tenth 0.3 three tenths 0.07 seven hundredths two hundred thirty-one thousandths twenty-five ten thousandths 2

3 Changing Decimal Numbers to Fractions A number can be written in many different forms. For example, the decimal number 0.5 is read as five tenths. In fraction form, it is: or This is referred to as a proper fraction, where the numerator (the number on top) of the fraction is smaller than its denominator (the number on bottom). Changing Decimal Numbers to Fractions A decimal number greater than 1, such as 3.5 is read as three and five tenths, and can also be written as the mixed number which combines a whole number and a proper fraction, This mixed number, can also be changed to an improper fraction where the numerator (top number) is larger than or equal to its denominator (bottom number). Example 1.1 Write 2.25 as an improper fraction. The number 2.25 is read as two and twenty-five hundredths and written. 3

4 Changing Fractions to Decimal Numbers Changing Fractions to Decimal Numbers To change a fraction to a decimal number, think of the fraction as a division problem. For example: means or Changing Fractions to Decimal Numbers Here are the steps for this division: Step One: Replace 2 with 2.0 and then place a decimal point directly above the decimal point in 2.0 4

5 Changing Fractions to Decimal Numbers Step Two: Perform the division. Therefore, Example 1.2 Write as a decimal number. means Step 1: Example 1.2 (continued) Step 2: Therefore, 5

6 Changing Fractions to Decimal Numbers Dividing Quickly with Multiples of Ten A quicker way to do is to divide 19.3 by 10 by moving the decimal point in the number one place to the left. Changing Fractions to Decimal Numbers This is done because there is one zero in 10 (tenths place). If you divide by any number that is a multiple of 10 (e.g. 100, 1000, etc., you would move the decimal number to the left once place for every zero. Rounding Decimal Numbers 6

7 Rounding Decimal Numbers Rounding is sometimes done so that you can use an approximate answer rather than an exact one. Rounding off results in an answer with the closest accuracy. For example, you might be asked to round off to the nearest tenth (one decimal place) Answer: 1.3 Rounding down a number to a particular place, means dropping all the digits after that place. In particular, to round down to the tenths place, drop all the digits after the tenths place. Answer: 1.2 Example 1.3 (a) Round off to the nearest hundredth, tenth, and whole number Rounded off to the nearest: hundredth = 3.26 tenth = 3.3 whole number = 3 Example 1.3 (continued) (b) Round down to the nearest hundredth, tenth, and whole number Rounded down to the nearest: hundredth = 3.26 tenth = 3.2 whole number = 3 7

8 Rounding Decimal Numbers Unless otherwise specified, quantities less than 1 will be rounded to the nearest hundredth, while quantities greater than 1 will be rounded to the nearest tenth. Since the danger of an overdose must always be guarded against, the amount of medication to be administered is often rounded down instead of rounded off. This is done routinely in pediatrics, and when administering high-alert drugs to adults. Multiplying and Dividing Decimal Numbers & Whole Numbers Example x 0.16 =? So, =

9 Example =? There are three zeros in 1000, so move the decimal point in three places to the right. or Therefore, = 23,597 Example 1.6 Note that there are three decimal places in 0.002, so move the decimal points in both numbers three places to the right in both the numerator and denominator. means or Example 1.6 (continued) Therefore: 9

10 Multiplying and Dividing Fractions Example 1.7 Example 1.7 (continued) It is often convenient to cancel before you multiply. 10

11 Example 1.8 Write as the fraction Division Becomes the multiplication Example 1.9 Example

12 Multiplying and Dividing Fractions The numerator of this fraction is 0.35, a decimal number. You can write an equivalent form of the fraction by multiplying the numerator and denominator by 100. Complex Fractions Complex Fractions Complex fractions have fractions in their numerators and/or fractions in their denominators. A longer fraction line separates the numerator from the denominator, and indicates division. 12

13 Example 1.11 Example 1.11 (continued) Write as numerator denominator. Percentages 13

14 Example 1.12 Write 0.5% as a fraction. Example 1.12 (continued) There is another way to get the answer. You know that 0.5 =. Therefore, Chapter Summary When working with fractions: Proper fractions have smaller numbers in the numerator than in the denominator. Improper fractions have numerators that are larger than or equal to their denominators. Improper fractions can be changed to mixed numbers, and vice versa. Any number can be changed into a fraction by writing the number over 1. 14

15 Chapter Summary (continued) When working with fractions: Cancel first when you multiply fractions. Change a fraction to a decimal number by dividing the numerator by the denominator. Simplify complex fractions by dividing the numerator by the denominator. Chapter Summary (continued) When working with decimals: Move the decimal point 3 places to the right when multiplying a decimal number by 1,000. Move the decimal point 3 places to the left when dividing a decimal number by 1,000. Count the total number of places in the numbers you are multiplying to determine the number of decimal places in the answer. Avoid cancelling with decimal numbers. Chapter Summary (continued) When working with percentages: Change to fractions or decimal numbers before doing any calculations. 15