1. Chapter 2 Decimals
PowerPoint® Presentation to accompany:
Math and Dosage Calculations for Healthcare Professionals
Fourth Edition
Booth, Whaley, Sienkiewicz, and Palmunen

2. Learning Outcomes 2-1 Write decimals and compare their value.
2-2 Apply the rules for rounding decimals.
2-3 Convert fractions into decimals.
2-4 Convert decimals into fractions.

3. Learning Outcomes (cont.)
2-5 Add and subtract decimals.
2-6 Multiply decimals.
2-7 Divide decimals.

4. Key Terms Divisor Dividend Quotient
Divisor – The number you are dividing by.
Dividend – The number you are dividing into.
Quotient – The answer when dividing.

5. Introduction
Many of the math skills used for fractions are used for numbers containing decimals.
It is important to be comfortable working with decimals when performing dosage calculations.

6. Decimals
Decimals are another way to represent whole numbers and their fractional parts.
They are used daily by Healthcare practitioners.
The Metric System
is decimal based;
is used in dosage calculations, calibrations, and charting.
Learning Outcome: 2-1 Write decimals and compare their value.
It is important for the medical assistant to be able to work with decimals and convert fractions and mixed numbers to decimals.

7. Decimals (cont.)
The location of a digit relative to the decimal point determines its value.
The decimal point separates the whole number from the decimal fraction.
Learning Outcome: 2-1 Write decimals and compare their value.

8. Decimals (cont.) 1, 5 4 2 6 7 1, 5 4 2 6 7 Decimal Place Values
The number 1, can be represented as follows:
Whole Number
Decimal Point
Decimal Fraction
Thousands
Hundreds
Tens
Ones .
Tenths
Hundredths
Thousandths 1, 5 4 2 6 7
Thousands
Hundreds
Tens
Ones .
Tenths
Hundredths
Thousandths 1, 5 4 2 6 7
Learning Outcome: 2-1 Write decimals and compare their value.
Each position of a decimal number has a place value.
The places to the right of a decimal point represent fractions.

9. Decimal (cont.) The number 1,542.567 is read:
(1) – one thousand
(5) – five hundred
(42) – forty two and
(0.5) – five hundred
(0.067) – sixty-seven thousandths
One thousand five hundred forty two and five hundred sixty-seven thousandths
Learning Outcome: 2-1 Write decimals and compare their value.

10. Writing Decimals Rule 2-1 When writing a decimal number:
Write the whole number part to the left of the decimal point.
Write the decimal fraction part to the right of the decimal point.
Learning Outcome: 2-1 Write decimals and compare their value.
Decimal fractions are equivalent to fractions that have denominators of 10, 100, 1000, and so forth.
A zero is used as a place holder if there is no whole number.

11. Writing Decimals Rule 2-1 When writing a decimal number:
Use zero as a placeholder to the right of the decimal point.
Example: 0.201
Learning Outcome: 2-1 Write decimals and compare their value.
A zero is used as a place holder if there is no whole number.

12. Writing Decimals (cont.)
Rule 2-2 Always write a zero to the left of the decimal point when the decimal number has no whole number part.
This helps to prevent errors caused by illegible handwriting.
Learning Outcome: 2-1 Write decimals and compare their value.
Always write 0.5 not .5
Do not write 5.0
The leading zero makes the decimal point more noticeable.

13. Comparing Decimals
Rule 2-3 To compare values of a group of decimal numbers:
The decimal with the greatest whole number is the greatest decimal number.
If the whole numbers are equal, compare the digits in the tenths place.
Learning Outcome: 2-1 Write decimals and compare their value.

14. Comparing Decimals
Rule 2-3 To compare values of a group of decimal numbers: (cont.)
If the tenths place digits are equal, compare the hundredths place digits.
Continue moving to the right comparing digits until one is greater than the other.
Learning Outcome: 2-1 Write decimals and compare their value.

15. Comparing Decimals (cont.)
The more places a number is to the right of the decimal point the smaller the number’s value.
Examples
0.3 is or three tenths
Learning Outcome: 2-1 Write decimals and compare their value.
0.03 is or three hundredths
0.003 is or three thousandths

16. Practice
Write the following in decimal form:
Answers
= 0.2
= 0.17
Learning Outcome: 2-1 Write decimals and compare their value.
= 0.023

17. Rounding Decimals Rule 2-4 Underline the place value.
Look at the digit to the right of this target.
Drop all digits to the right of the target place value.
Learning Outcome: 2-2 Apply the rules for rounding decimals.
2. If the digit to the right of the target is 4 or less, do not change the digit; if it is 5 or more, round up one unit.
Decimals are usually rounded to the nearest tenth or hundredth.

18. Practice Answer 14.3 Answer 9.3 Answer 8.80 Answer 10.54
Round to the nearest tenth:
14.34
9.293
Round to the nearest hundredth:
8.799
10.542
Answer 14.3
Answer 9.3
Learning Outcome: 2-2 Apply the rules for rounding decimals.
Problem 1
The target place value is the tenths place. The digit to the right of this is a 4, so the 3 in the tenths place does not change value.
Problem 2
The target place value is the tenths place. The digit to the right of this is a 9, so the 2 in the tenths place becomes a 3.
Problem 3
The target place value is the hundredths place . The digit to the right of this is a 9, so the 9 in the hundredths is increased to 10 and the one is carried back to the tenths place where the 7 becomes an 8.
Problem 4
The target place value is the hundredths place. The digit to the right of this is a 2 so the 4 does not change.
Think!…Is It Reasonable?
Answer 8.80
Answer 10.54

19. Converting Fractions into Decimals
Rule 2-5
To convert a fraction to a decimal, divide the numerator by the denominator.
Example
Learning Outcome: 2-3 Convert fractions into decimals.
Think of the fraction as a division problem.
Reducing the fraction first may make the problem easier.
Think!…Is It Reasonable?

20. Converting Decimals into Fractions (cont.)
Rule 2-6
Write the number to the left of the decimal point as the whole number.
Write the number to the right of the decimal point as the numerator of the fraction.
Learning Outcome: 2-4 Convert decimals into fractions.

21. Converting Decimals into Fractions (cont.)
Rule 2-6 (cont.)
Use the place value of the digit farthest to the right of the decimal point as the denominator.
Reduce the fraction part to its lowest term.
Learning Outcome: 2-4 Convert decimals into fractions.

22. Practice
Convert decimals to fractions or mixed numbers and reduce to lowest terms:
1.2
Answer or
100.45
Answer or
Learning Outcome: 2-4 Convert decimals into fractions.
Problem 1
The 2 is in the tenths place.
1.2 = 1 2/10 = 1 1/5
Problem 2
The 5 is in the hundredths place.
= /100 = 100 9/20
Think!…Is It Reasonable?

23. Adding and Subtracting Decimals
Rule 2-7
Write the problem vertically. Align the decimal points.
Add or subtract starting from the right. Include the decimal point in your answer.
2.47
+ 0.39
2.86
Learning Outcome: 2-5 Add and subtract decimals.

24. Adding and Subtracting Decimals (cont.)
Examples
Subtract
7.3 – 1.005
Answer:
7.300
6.295
Add
Answer:
13.561
13.660
Learning Outcome: 2-5 Add and subtract decimals.
Think!…Is It Reasonable?

25. Practice Add or subtract the following pair of numbers: 48.669 + 0.081
Answer
16.25 – 1.625
Answer
Learning Outcome: 2-5 Add and subtract decimals.
Problem 1
48.669
48.750
Problem 2
16.250
14.625
Think!…Is It Reasonable?

26. Multiplying Decimals Rule 2-8 (cont.)
First, multiply without considering the decimal points, as if the numbers were whole numbers.
Count the total number of places to the right of the decimal point in both factors.
Learning Outcome: 2-6 Multiply decimals.
Multiplication of decimals is similar to multiplying whole numbers.
However, you must determine the proper position of the decimal place.

27. Multiplying Decimals Rule 2-8 (cont.)
To place the decimal point in the product, start at its right end and move the it to the left the same number of places.
Learning Outcome: 2-6 Multiply decimals.

28. Multiplying Decimals (cont.)
Multiply 3.42 x 2.5
3.42
X 2.5
1710
684
8550
There are three decimal places, so place the decimal point between 8 and 5.
Answer: 8.55
Example
Learning Outcome: 2-6 Multiply decimals.
Think!…Is It Reasonable?

29. Practice
A patient is given 7.5 milliliters of liquid medication 5 times a day. How may milliliters does she receive per day?
Answer x 5
7.5
X 5
37.5
Learning Outcome: 2-6 Multiply decimals.
7.5 mL
X 5 times daily
375
There is 1 decimal place in the problem, so the decimal is place between the 7 and 5.
Think! !…Is It Reasonable?

30. Dividing Decimals Rule 2-9
Move the decimal point to the right the same number of places in both the divisor and dividend until the divisor is a whole number.
Learning Outcome: 2-7 Divide decimals.
The dividend is the number you are dividing into.
The divisor is the number you are dividing by.
Insert zeros as needed.

31. Dividing Decimals Rule 2-9 (cont.)
2. Complete the division as you would with whole numbers.
Align the decimal point of the quotient with the decimal point of the numerator.
Learning Outcome: 2-7 Divide decimals.

32. Dividing Decimals (cont.)
Example
Divide
(1)  (2) 6.6  11
Learning Outcome: 2-7 Divide decimals.
1 – Move the decimal point the same number of places to the right in both the divisor and dividend until the divisor is a whole number.
Think!…Is It Reasonable?

33. Practice
A bottle contains 32 ounces of medication. If the average dose is 0.4 ounces, how many doses does the bottle contain?
Answer: 80
Learning Outcome: 2-7 Divide decimals.
32  0.4 = 320  4 = 80
Think!…Is It Reasonable?

34. In Summary In this chapter you learned to:
write decimals and compare their value;
apply rules for rounding decimals;
convert fractions to decimals.
The places to the right of a decimal represent fractions, and each position has a place value.
First compare the value of the numbers to the left of the decimal.
When the numbers to the left of the decimal are the same, compare values to the right of the decimal, moving one place at a time until finding one value greater than another.
When rounding, look at the first digit to the right of the place value that you are rounding to.
If this digit is 5 or more, round up.
If it is less than 5, round down.
To convert a fraction to a decimal, divide the numerator by the denominator.

35. In Summary (cont.) In this chapter you learned to:
convert decimals into fractions;
add and subtract decimals;
multiply decimals;
divide decimals.
To convert a decimal to a fraction, write the numbers to the right of the decimal as the numerator and the place value of the number furthest to the right as the denominator.
To add and subtract decimals, it is first necessary to align the decimals vertically before adding or subtracting.
To multiply decimals, first multiply the numbers, then determine the position of the decimal.
The decimal in your answer should be placed so that the number of digits to the right of the decimal is equal to the total number of decimal places in the numbers that were multiplied.
To divide decimals, write the problem as a fraction with the dividend as the numerator and the divisor as the denominator.
Move the decimal to the right in both parts of the fraction until the denominator is a whole number, and then perform the division.

36. Apply Your Knowledge Round to the nearest tenth: 7.091 Answer 7.1
Learning Outcome: 2-2 Apply the rules for rounding decimals.
The number to the right of the selected place value is > 5, so the number in the selected place value is increased.
Think!…Is It Reasonable?

37. Apply Your Knowledge Add the following: 7.23 + 12.38
Answer
Multiply the following: x 1.005
Learning Outcome: 2-5 Add and subtract decimals.
Learning Outcome: 2-6 Multiply decimals.
Problem 1
7.23
+12.38
19.61
Problem 2
12.01 X
6005
Count the number of decimal places = 5
Answer =
Think!…Is It Reasonable?
Answer

38. End of Chapter 2
Learning is not attained by chance, it must be sought for with ardor and attended to with diligence.
-Abigail Adams