Dimensional Analysis

Lecture 1Chapter 1

Relative value of decimals

• 0 0 0 0 0 0 0 . 0 0 0Whole numbers fractions

• Example20.2 > 8.26

Your turn!

• Identify the number with the highest value1. a) 11.8 b) 10.7 c) 9.062. a) 8.99 b) 6.09 c) 12.33. a) 0.475 b) 2.06 c) 1.39

Key Concept

• If a decimal fraction is not preceded by a whole number, a zero is used in front of the decimal point to emphasize that the number is a fraction.

• Example– . 246 0.246– .12 0.12– .9 0.9

Key Concept

• When the whole numbers are identical, the fraction with the higher number representing tenths has the higher value

• Example– 15.7 > 15.3– 0.4 > 0.37– 0.6> 0.582

Your Turn

• Which decimal has the highest value?1. a) 5.5 b) 5.75 c) 5.252. a) 1.01 b) 1.1 c) 1.023. a) 0.41 b) 0.35 c) 0.5

Your Turn

• Which decimal has the highest value?1. a) 5.5 b) 5.75 c) 5.252. a) 1.01 b) 1.1 c) 1.023. a) 0.41 b) 0.35 c) 0.5

(There are more problems like this on page 5 of your text book)

Key Concept

• When the whole numbers and the tenths are identical, the decimal fraction with the highest number representing hundreths will have the higher value.

• 0.27 is higher than 0.25• 0.15 is higher than 0.1 (0.1 = 0.10)

• You can add zeros to the end of a fraction decimal without changing the value.– $1 = $1.00– 0.1 = 0.1000000000

• (Key) extra zeros on the end of decimal fractions are omitted in drug dosages because they can easily be misread.

Key Concept

• The number of figures on the right of the decimal point is not an indication of relative value. Always look at the figure representing the tenths first, and if these are identical, look at the hundredth to determine which has the higher value.

• Which fraction has the higher value?

1. a) 0.123456789 b) 0.21

Key Concept

• The number of figures on the right of the decimal point is not an indication of relative value. Always look at the figure representing the tenths first, and if these are identical, look at the hundredth to determine which has the higher value.

• Which fraction has the higher value?1. a) 0.123456789 b) 0.21• More problems on page 6

Addition and subtraction of Decimals

• (key) when you write the number down, line up the decimal points.

• To add 1.25 + 0.351.25

+ 0.321.57

• For the Dimensional Analysis Quiz 1 you will not be allowed to use any calculator or cell phones.

• (key) always add or subtract from right to left.– 0.47 + 0.24– 0.82 – 0.74

0.47 0.82+ 0.24 - 0.74 0.71 0.08

• (key) add zeros as necessary to make the fractions equal in length.0.46 0.460

- 0.123 - 0.123

Your Turn

• Calculate the following (no calculators!)1. 0.36 + 0.66 = 2. 0.01 + 2.78 =3. 2.25 – 2.125 = 4. 4.36 – 0.74 =

Your Turn

• Calculate the following (no calculators!)1. 0.36 + 0.66 = 1.022. 0.02 + 2.78 = 2.80 2.83. 2.25 – 2.125 = 0.1254. 4.36 – 0.74 = 3.62

Applied math

• You have a bottle of medication and each pill in the bottle has a strength of 1mg. The doctor orders the patient to be given 5mg of the medications. You will need to give then…

A.1 tabletB.Less than 1 tabletC.More than 1 tablet

Applied math

• You have a bottle of medication and each pill in the bottle has a strength of 3mg. The doctor orders the patient to be given 1mg of the medications. You will need to give then…

A.1 tabletB.Less than 1 tabletC.More than 1 tablet

Applied Math

• If you have medication tablets whose strength is 0.1 mg and you must give 0.3 mg, you will need…

A) 1 tabletB) Less than 1 tabletC) More than 1 tablet

• If you have medication tablets whose strength is 0.25 mg and you must give 0.125 mg, you will need…

A) 1 tabletB) Less than 1 tabletC) More than 1 tablet

• You have just given two tablets with a dosage strength of 2.5 mg each. What was the total dosage administered?– 2.5 mg + 2.5 mg = 5 mg

• You are given one tablet labeled 0.6 mg and two tablets labeled 0.2 mg. What is the total dosage?– 0.6 mg + 0.2 mg + 0.2 mg = 1 mg

Sample Dimensional Analysis Quiz #1

• Choose the decimal with the highest valueA) 4.44B) 4.57C) 4.19

Sample Dimensional Analysis Quiz #1

2. The order is to give 0.5 mg and the tablets have a strength of 0.25 mg. You must give…

A) 1 tabletB) Less than 1 tabletC) More than 1 tablet

Sample Dimensional Analysis Quiz #1

3. Add the decimal1.59 + 0.6 =

Sample Dimensional Analysis Quiz #1

4. You have two tablets with a dose strength of 0.25 mg. What was the total dosage given?

5. Subtract the decimal3.82 – 1.75 =