Transcript Dimensional Analysis - Porterville College

Dimensional Analysis
Lecture 1
Chapter 1
Relative value of decimals
• 0 0 0 0 0 0 0 . 0 0 0
Whole numbers
• Example
20.2 > 8.26
fractions
Your turn!
•
1.
2.
3.
Identify the number with the highest value
a) 11.8
b) 10.7
c) 9.06
a) 8.99
b) 6.09
c) 12.3
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
•
1.
2.
3.
Which decimal has the highest value?
a) 5.5
b) 5.75
c) 5.25
a) 1.01 b) 1.1
c) 1.02
a) 0.41 b) 0.35
c) 0.5
Your Turn
•
1.
2.
3.
Which decimal has the highest value?
a) 5.5
b) 5.75
c) 5.25
a) 1.01 b) 1.1
c) 1.02
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 + 0.35
1.25
+ 0.32
1.57
• 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
+ 0.24
0.71
-
0.82
0.74
0.08
• (key) add zeros as necessary to make the
fractions equal in length.
0.46
 0.460
- 0.123
- 0.123
Your Turn
•
1.
2.
3.
4.
Calculate the following (no calculators!)
0.36 + 0.66 =
0.01 + 2.78 =
2.25 – 2.125 =
4.36 – 0.74 =
Your Turn
•
1.
2.
3.
4.
Calculate the following (no calculators!)
0.36 + 0.66 = 1.02
0.02 + 2.78 = 2.80  2.8
2.25 – 2.125 = 0.125
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 tablet
B. Less than 1 tablet
C. 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 tablet
B. Less than 1 tablet
C. 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 tablet
B) Less than 1 tablet
C) 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 tablet
B) Less than 1 tablet
C) 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
•
A)
B)
C)
Choose the decimal with the highest value
4.44
4.57
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 tablet
B) Less than 1 tablet
C) More than 1 tablet
Sample Dimensional Analysis Quiz
#1
3. Add the decimal
1.59 + 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 decimal
3.82 – 1.75 =