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Chapter 2 Decimals

PowerPoint® Presentation to accompany:

Math and Dosage Calculations for Healthcare Professionals

Fourth Edition

Booth, Whaley, Sienkiewicz, and Palmunen

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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.

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Learning Outcomes (cont.)

2-5 Add and subtract decimals.

2-6 Multiply decimals.

2-7 Divide decimals.

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Key Terms Divisor

Dividend

Quotient

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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.

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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.

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The location of a digit relative to the decimal point determines its value.

The decimal point separates the whole

number from the decimal fraction.

Decimals (cont.)

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Decimal Place Values

The number 1,542.567 can be represented as follows:

Whole Number Decimal Point

Decimal Fraction

Thousands Hundreds Tens Ones . Tenths Hundredths Thousandths

1, 5 4 2 . 5 6 7

Decimals (cont.)

Thousands Hundreds Tens Ones . Tenths Hundredths Thousandths

1, 5 4 2 . 5 6 7

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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

Decimal (cont.)

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Writing Decimals

Rule 2-1Rule 2-1 When writing a decimal number:1. Write the whole number part to the left of

the decimal point.

2. Write the decimal fraction part to the right of the decimal point.

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Writing Decimals

Rule 2-1Rule 2-1 When writing a decimal number:3. Use zero as a placeholder to the right of

the decimal point.

Example: 0.201

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Rule 2-2 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.

Writing Decimals (cont.)

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Rule 2-3Rule 2-3 To compare values of a group of decimal numbers:

1. The decimal with the greatest whole number is the greatest decimal number.

2. If the whole numbers are equal, compare the digits in the tenths place.

Comparing Decimals

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Comparing Decimals

Rule 2-3Rule 2-3 To compare values of a group of decimal numbers: (cont.)

3. If the tenths place digits are equal, compare the hundredths place digits.

4. Continue moving to the right comparing digits until one is greater than the other.

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The more places a number is to the right of the decimal point the smaller the number’s value.

0.3 is or three tenths103

0.03 is or three hundredths1003

0.003 is or three thousandths10003

Comparing Decimals (cont.)

Examples Examples

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Practice

Write the following in decimal form:

102

10017

100023

Answers = 0.2

= 0.17

= 0.023

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Rounding Decimals

Rule 2-4Rule 2-41. Underline the place value.

2. Look at the digit to the right of this target.

3. Drop all digits to the right of the target place value.

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PracticeRound to the nearest tenth:

14.34

9.293

Round to the nearest hundredth:

8.799

10.542

Answer 9.3

Answer 14.3

Answer 10.54

Answer 8.80

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Converting Fractions into Decimals

Rule 2-5Rule 2-5

To convert a fraction to a decimal, divide the numerator by the denominator.

0.7543

1.658

Example Example

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Converting Decimals into Fractions (cont.)

Rule 2-6Rule 2-61. Write the number to the left of the decimal

point as the whole number.

2. Write the number to the right of the decimal point as the numerator of the fraction.

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Converting Decimals into Fractions (cont.)

Rule 2-6 Rule 2-6 (cont.)

3. Use the place value of the digit farthest to the right of the decimal point as the denominator.

4. Reduce the fraction part to its lowest term.

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Practice

Convert decimals to fractions or mixed numbers and reduce to lowest terms:

100.45

1.2 Answer51

1 or

Answer209

100 or

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Adding and Subtracting Decimals

Rule 2-7Rule 2-71. Write the problem vertically. Align the decimal

points.

2. Add or subtract starting from the right. Include the decimal point in your answer.

2.47+ 0.39 2.86

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Adding and Subtracting Decimals (cont.)

Subtract 7.3 – 1.005

Answer:

7.300

- 1.005

6.295

Add

13.561 + 0.099

Answer:

13.561

+ 0.099

13.660

Examples Examples

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Practice

Add or subtract the following pair of numbers:

48.669 + 0.081

Answer 14.625

Answer 48.75

16.25 – 1.625

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Multiplying Decimals

Rule 2-8 Rule 2-8 (cont.)

1. First, multiply without considering the decimal points, as if the numbers were whole numbers.

2. Count the total number of places to the right of the decimal point in both factors.

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Multiplying Decimals

Rule 2-8 Rule 2-8 (cont.)

3. 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.

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Multiply 3.42 x 2.5 3.42X 2.5 1710684 8550

There are three decimal places, so place the decimal point between 8 and 5.

Answer: 8.55

Multiplying Decimals (cont.)

ExampleExample

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Practice

A patient is given 7.5 milliliters of liquid medication 5 times a day. How may milliliters does she receive per day?

Answer 7.5 x 5

7.5X 537.5

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Rule 2-9Rule 2-9

1. 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.

Dividing Decimals

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Dividing Decimals

Rule 2-9 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.

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Dividing Decimals (cont.)

Divide

(1) 0.066 0.11 (2) 6.6 11

0.66.611 3

ExampleExample 0.11 0.066

0.60.11 0.066

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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

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In Summary In this chapter you learned to:

write decimals and compare their value;

apply rules for rounding decimals;

convert fractions to decimals.

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In Summary (cont.)

In this chapter you learned to:

convert decimals into fractions;

add and subtract decimals;

multiply decimals;

divide decimals.

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Apply Your Knowledge

Round to the nearest tenth:

Answer 7.1

7.091

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Apply Your Knowledge

Add the following: 7.23 + 12.38

Multiply the following: 12.01 x 1.005

Answer 19.61

Answer 12.07005

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End of Chapter 2

Learning is not attained by chance, it must be sought for with ardor and attended to with diligence.

-Abigail Adams