Objectives Chapter 3 Read and write decimal numbers Compare decimals Read syringes in decimals Add decimal numbers Subtract decimal numbers Multiply decimal numbers Divide decimal numbers, including using zero as a place holder Calculate decimal numbers in word problems Use simplified multiplication and division Convert scale units from decimals to fractions Convert fractions to decimal numbers and vice versa Convert Celsius to Fahrenheit temperatures Solve mixed fraction and decimal number problems Round decimals to a specific place value

Decimals are used every day in health care settings Decimals are used every day in health care settings. Understanding the application of decimals provides a strong foundation for measurement conversions, the metric system, medication dosages, and general charting work. Most medication orders are written using the metric system, which relies on decimals. Decimals Decimal place values must be understood for all health care applications because decimals are used every day in health care settings. Understanding the application of decimals provides a strong foundation for dealing with measurement conversions, the metric system, medication dosages, and general charting work. Students know that the average temperature for human beings is 98.6°F, but they may not see this as a decimal number. In addition, most medication orders are written using the metric system, which relies on decimals. Decimals also appear on drug labels, providing the details about the amount of a medication in metric units per tablet or capsule. These amounts may appear as a decimal number plus “milligram/tablet” or simply as a decimal number, as shown in the labels below. (Point out that not all medications have decimal numbers.) Decimals also appear on digital scales measuring patient weights. Pages 70 - 93

Page 75 Decimals A decimal represents a part or fraction of a whole number. Decimal numbers are parts of 10s, 100s, 1000s, and so on. In other words, decimals are multiples of ten. The decimal point (.) represents the boundary between whole numbers and decimal numbers.

Decimal Place Value Page 75 Whole Numbers Decimal Numbers thousands   Decimal Numbers thousands hundreds tens ones and tenths hundredths thousandths ten-thousandths hundred-thousandths 1 4 . 9 3 5 Reading decimal numbers is simple if you follow these steps: To read decimal numbers, say the numbers from left to right as if they were whole numbers, then and the decimal place value. Identify decimal numbers by looking for the words that end in the “th” or “ths” *** Examples – Pages 76-77 – practice 1-2: evens Group Work – Pages 76-77 – practice 1-2: odds

Page 78 Rounding Decimal Decimals are rounded in health care to create manageable numbers. We may have a difficult time visualizing a number such as 14.39757. However, we can easily understand the number 14.4 or 14.40. Rounding to a specific decimal place is accomplished in the same way that whole numbers are rounded. In general, health care workers round decimal numbers to the nearest tenth or the nearest hundredth. Underline the place to which you are rounding Circle one number to the right of the underlined number. If the circled number is 5 or greater, add 1 to the underlined number, and drop all the numbers to the right of the changed number If the circled number is less than 5, do not change the underlined number, and drop all the numbers to the right of that number *** Examples – Pages 78-79 – practice 3-4: evens Group Work – Pages 78-79 – practice 3-4: odds

Comparing Decimals Page 79 Comparing decimals is valuable in health occupations because many different pieces of equipment are used that may be in metric measurements. Decimals are part of the metric system; thus understanding them is necessary to determine which instrument or measurement is larger or smaller. Comparing decimals is a skill that is also useful in sorting and ordering inventory items by size. To compare decimals, you will rely on your eyes rather than any specific math computation. Examples – Pages 80-81 – practice 5-8: evens Group Work – Pages 80-81 – practice 5-8: odds

Addition of Decimals Page 82 To add decimals: Line up the decimals. (This might mean that the problem presented in a horizontal pattern may need to be rewritten in a vertical pattern.) The order or the numbers to be added is unimportant. Add the numbers and bring the decimal point straight down. Examples – Pages 82-83 – practice 9-10: evens Group Work – Pages 82-83 – practice 9-10: odds

Subtraction of Decimals Page 83 Subtraction of Decimals To subtract decimals: Set the problem up vertically. Put the number from which the second number is to be subtracted above, then line up the decimals. Subtract and then bring the decimal straight down. Examples – Pages 83-84 – practice 11-12: evens Group Work – Pages 83-84 – practice 11-12: odds

Multiplication of Decimals Pages 84 – 85 Multiplication of Decimals To multiply decimals: Write the problem vertically. Multiply the numbers (just like in whole number multiplication) Do not line up the decimals Count the total number of decimal places in the two factors. Then begin at the right of the product and count over the same number of places and place the decimal point. Examples – Pages 85-86 – practice 13-14: evens Group Work – Pages 85-86 – practice 13-14: odds

Division of Decimals Page 87 To divide decimals, one needs to place the decimal point, then divide the numbers. Move the decimal point straight up to the same place in the quotient (answer). Divide, adding a zero in front of all decimal numbers that do not include a whole number. Examples – Pages 87 – practice 15: evens Group Work – Pages 87 – practice 15: odds

Zeros as Placeholder in Decimal Division Page 88 Zeros as Placeholder in Decimal Division Recall that after a number has been brought down from the dividend, the divisor must be applied to that number. Place the decimal point and then divide the number. If the divisor does not go into the dividend, then a zero must be placed in the quotient. Use a zero to hold a space.

Divide Decimals By Decimals Page 88 Divide Decimals By Decimals To divide a decimal number by a decimal number: Change the divisor to a whole number by moving the decimal point to the right. Move the decimal point in the dividend the same number of places. Use zeros as place holders if needed. Place the decimal point and divide. Examples – Pages 88-89 – practice 16-17: evens Group Work – Pages 88-89 – practice 16-17: odds

Simplified Multiplication & Division of Decimals Pages 89 – 91 Simplified Multiplication & Division of Decimals This shortcut works with multiples of ten: 10, 100, 1,000, etc. The process is straightforward. To multiply, move the decimal point to the right. To divide, move the decimal point to the left. The number of spaces depends on which multiple you are working with. Look at the number of zeros included in the multiple, then move the decimal in either direction depending on the operation: multiplication or division, the same number of spaces and the number of zeros. In health-care fields, this shortcut is important to your work in metrics and in efficiently working longer problems. ***** Examples – Pages 90-92 – practice 18-20: evens Group Work – Pages 90-92 – practice 18-20: odds

Changing Decimals to Fractions Pages 92 – 93 Changing Decimals to Fractions It is important to be able to convert between number systems so that you are comfortable with comparing sizes of items or quantities of supplies. Changing decimals to fractions requires the use of decimal places and placing the numbers in fractions that represent the very same numbers. Examples – Pages 93-94 – practice 21: evens Group Work – Pages 93-94 – practice 21: odds

Changing Fractions to Decimals Pages 94 – 95 Changing Fractions to Decimals To change fractions to decimals, divide the denominator into the numerator. Critical to the success of this division is the placement of the decimal point. Once it is placed, do not move it. Examples – Pages 95-96 – practice 22: evens Group Work – Pages 95-96 – practice 22: odds

Temperature Conversions with Decimals Page 96 – 97 Temperature Conversions with Decimals The temperature conversion used in Unit 2: Fractions, relied on fractions. The same conversion can be done with a decimal method. (℃ x 1.8) + 32 = oF (oF – 32) ÷ 1.8 = ℃ In deciding which method to use, base it on your strongest skill. Examples – Pages 97 – practice 23: evens Group Work – Pages 97 – practice 23: odds

Solving Mixed Fractions & Decimals Problems Pages 97 – 98 Solving Mixed Fractions & Decimals Problems If the problem has a complex fraction multiplied by a decimal number, work the complex fraction first. Then complete the decimal multiplication. If the problem includes a decimal number, solve the decimals by first multiplying straight across, then complete the process by dividing that answer by the denominator. This allows for the division of decimals only once, and it saves time. Examples – Pages 99 – practice 24: evens Group Work – Pages 99 – practice 24: odds