Transcript Dimensional Analysis #2

Dimensional Analysis
Lecture 2
Chapter 2
Review Question
• Which of the following decimal numbers are
NOT written correctly for nursing charting?
A. 1.2
B. .12
C. 12.0
D. 0.012
Calculators!!
• Bring a calculator to class
• You may not use cell phones during tests
• You may not borrow a calculator from another
student until they have turned in their test
Multiplication of Decimals – Without a
calculator
• The decimal point in the product of decimal
fractions is placed the same number of places
to the left in the product, as the total number
after the decimal points in the fractions
multiplied.
– 0.42 x 0.6 =
0.42 (2 places to the left)
x 0.6 (1 place to the left)
252 (count 3 places to left)  .252
 0.252
Multiplication of Decimals –
with a calculator
– 0.42 x 0.6 =
•
•
•
•
•
Enter the number 0.42
Press the multiplication function (x)
Enter the number 0.6
Press the equal function (=)
Write down the answer
Multiplication of Decimals – Without a
calculator
• If the product contains insufficient numbers
for correct placement of the decimal point,
add as many zeros as necessary to the left of
the product to correct this
– 1.3 x 0.07
1.3 (1 place to the left)
x 0.07 (2 places to the left)
91 (count 3 places to the left)  .091
 0.091
Multiplication of Decimals –
With a calculator
– 1.3 x 0.07
Enter 1.3
Press the (x) button
Enter 0.07
Press the (=) button
Write down the answer
Multiplication of Decimals
• Example
– 1.08 x 0.05
•
1.08 (count 2 places)
x 0.05 (count 2 places)
540 (count 4 places)  .0540
 0.0540 (add a zero in front)
 0.054 (drop extra zero)
Multiplication of Decimals
• Example
– 1.08 x 0.05
– Enter 1.08
– Enter x
– Enter 0.05
– Press =
– Write down the answer
Calculate: 0.55 x 0.2 =
A.
B.
C.
D.
E.
11
1.1
0.11
0.011
None of the above
Calculate: 0.34 x 0.08 =
A.
B.
C.
D.
E.
0.0272
0.272
2.72
27.2
None of the above
Calculate: 1.16 x 0.05 =
A. 0.58
B. 5.8
C. 58
D. 580
E. None of the above
Need more practice?
1. 0.55 x 0.2
2. 0.34 x 0.08
3. 1.16 x 0.05
More problems like this on page 13 of
your text book!
Division of Decimal Fractions
0.25 = ____? _______(top #)
0.125 = ____?______(bottom #)
Division of Decimal Fractions
0.25 = numerator (top #)
0.125 = ____?___ (bottom #)
Division of Decimal Fractions
0.25 = numerator (top #)
0.125 = denominator (bottom #)
Division of Decimal Fractions
• 3 step process
1. Eliminate the decimal point
2. Reduction of numbers ending in zero
3. Reduction of numbers using common
denominator
Division of Decimal Fractions
Division of Decimal Fractions
• Look for which number has the must numbers
to the right of the decimal – start there.
• Count how many places you have to move the
decimal to the right before it is “gone”
• Move the decimal the same number of places
to the other number.
• What ever you do the numerator you must do
to the denominator
Division of Decimal Fractions
Division of Decimal Fractions
Division of Decimal Fractions
Division of Decimal Fractions
Division of Decimal Fractions
Division of Decimal Fractions
Division of Decimal Fractions
Division of Decimal Fractions
Eliminate the decimal point from
the decimal fraction
Eliminate the decimal point from
the decimal fraction
Eliminate the decimal point from
the decimal fraction
3.45 / 0.6
A. 345 / 6
B. 345 / 60
C. 345 / 600
D. 345 / 6000
Division of Decimal Fractions
• 3 step process
1. Eliminate the decimal point 
2. Reduction of numbers ending in zero
3. Reduction of numbers using common
denominator
Reduction of numbers ending in zero
• Numbers that end in zero or zero’s may
initially be reduced by crossing off the same
number of zeros in both the numerator and
denominator
– Example
500 =
20
Reduction of numbers ending in zero
• Numbers that end in zero or zero’s may
initially be reduced by crossing off the same
number of zeros in both the numerator and
denominator
– Example
500 = 500 =
20
20
Reduction of numbers ending in zero
• Numbers that end in zero or zero’s may
initially be reduced by crossing off the same
number of zeros in both the numerator and
denominator
– Example
500 = 500 = 50
20
20
2
Reduction of numbers ending in zero
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42
4000 4000
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42
4000 4000 40
Reduction of numbers ending in zero
Reduction of numbers ending in zero
Division of Decimal Fractions
• 3 step process
1. Eliminate the decimal point 
2. Reduction of numbers ending in zero P
3. Reduction of numbers using common
denominator
Reducing fractions
• To reduce fractions, divide the numerator and
the denominator by the highest common
denominator (the highest number that will
divide into both)
– Usually 2, 3, 4, 5
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Reducing fractions
Putting it all together!
Putting it all together!
Putting it all together!
Putting it all together!
Putting it all together!
Putting it all together!
Putting it all together!
Putting it all together!
Reduction of numbers ending in zero
• Example
4200 =
4000
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42 (2) = 21
4000 4000
40
20
Reduction of numbers ending in zero
• Example
4200 = 4200 =
4000 4000
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42 (?)
4000 4000
40
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42 (2) =
4000 4000
40
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42 (2) = 42/2
4000 4000
40
?
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42 (2) = 42/2 =
4000 4000
40
40/2
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42 (2) = 21
4000 4000
40
20
Reduction of numbers ending in zero
• Example
4200 = 4200 = 42 (2) = 21 = 1.05
4000 4000
40
20
Reduce the fractions as much as possible in
preparation for final division
Reduce the fractions as much as possible in
preparation for final division
Reduce the fractions as much as possible in
preparation for final division
Your Turn
• Reduce the fractions as much as possible in
preparation for final division
1. 40 / 16 (2)  20 / 8 (2)  10 / 4 (2)  5/2
2. 22 / 8 (2)  11 / 4
3. 66 / 8 (3)  22 / 9
4. 1450 / 1000 (5)  29 / 20
•
More problems like this on page 15 of your
text book
Division of Decimal Fractions
• 3 step process
1. Eliminate the decimal point
2. Reduction of numbers using common
denominator
3. Reduction of numbers ending in zero
Reduce the fraction to their lowest
terms in preparation for final division.
500 / 2500
A. 5 / 25
B. 1 / 5
C. 2 / 1
D. 5 / 1
E. None of the above
Reduce the fraction to their lowest
terms in preparation for final division.
400 / 150
A. 80 / 30
B. 4 / 15
C. 40 / 15
D. 4 / 5
E. None of the above
Reduce the fraction to their lowest
terms in preparation for final division.
210,000 / 600,000
A. 21 / 60
B. 2 / 6
C. 7 / 20
D. 6 / 21
E. None of the above
Your turn!
• Reduce the fraction to their lowest terms in
preparation for final division.
1. 500 = 500 = 5 (5) = 1
2500 2500 25
5
2. 400 = 400 = 40 (5) 8
150 150
15
3
3. 210,000 = 210,000 = 21 (3) = 7
600,000 600,000 60
20
More problems on page 16 of your text
Expressing to the nearest tenth
• 1234.567
– 5 is in the tenth place
– 6 is in the hundredth place
– 7 is in the thousandth place
– . Decimal point
– 4 is in the ones place
– 3 is in the tens place
– 2 is in the hundreds place
– 1 is in the thousands place
Expressing to the nearest tenth
• To express an answer to the nearest tenth, the
division is carried to hundredths (2 places
after the decimal). When the number
representing hundredth is 5 or larger, the
number representing tenths is increased by
one.
– Example
• 1.66 
– 1.7
Expressing to the nearest tenth
• Example
1. 1.16 
– 1.2
2. 6.22
– 6.3
3. 1.98
– 2.0  2
Express your answer to the nearest
tenths
7.598111
A. 7.5
B. 7.6
C. 7.50
D. 7.59
E. 7
Express your answer to the nearest
tenths
1.454545
A. 1.4
B. 1.5
C. 1.45
D. 1.6
E. 1
Express your answer to the nearest
tenths
1.838383
A. 1.8
B. 1.9
C. 1.7
D. 1.83
E. 2
Express your answer to the nearest
tenths
2.976543
A. 2.9
B. 2.97
C. 2.8
D. 3.0
E. 3
Express your answer to the nearest
tenths
5.038578
A. 5.0
B. 5.1
C. 5.03
D. 5.2
E. None of the above
Your turn
• You did a problem on the calculator and the
answer came out as follows. Express your
answer to the nearest tenths.
1. 7.598111  7.6
2. 1.454545  1.5
3. 1.838383  1.9
4. 2.976543  3.0  3
5. 5.038578  5.0  5
Some harder questions?
• You did a problem on the calculator and the
answer came out as follows. Express your
answer to the nearest tenths.
1. 1
2. 2.01
3. 3.00009
4. 40
5. 500
Some harder questions?
• You did a problem on the calculator and the
answer came out as follows. Express your
answer to the nearest tenths.
1. 1  1
2. 2.01  2
3. 3.00009  3
4. 40  40
5. 500  500
Expressing to the nearest hundredth
• 1234.567
– 5 is in the tenth place
– 6 is in the hundredth place
– 7 is in the thousandth place
– . Decimal point
– 4 is in the ones place
– 3 is in the tens place
– 2 is in the hundreds place
– 1 is in the thousands place
Expressing to the nearest hundredth
• To express an answer to the nearest
hundredth, the division is carried to the
thousandths (3 places after the decimal
point). When the number representing the
thousandth is 5 or larger, the number
representing the hundredths is increased by
one.
– Example
• 0.893
–  0.89
Expressing to the nearest hundredth
• Example
– 0.666 
• 0.67
– 0.836 
• 0.84
– 0.958 
• 0.96
– 0.999 
• 1.0  1
Express the numbers to the
nearest hundredth.
1.854
A. 1.8
B. 1.9
C. 1.85
D. 1.86
E. None of the above
Express the numbers to the
nearest hundredth.
2.165
A. 2.1
B. 2.2
C. 2.26
D. 2.27
E. None of the above
Express the numbers to the
nearest hundredth.
0.507
A. 0.5
B. 0.50
C. 0.51
D. 0.57
E. None of the above
Express the numbers to the
nearest hundredth.
3.496
A. 3.5
B. 3.49
C. 3.46
D. 3.4
E. None of the above
Your turn!
• Express the numbers to the nearest hundredth.
1. 1.854
–
 1.85
2. 2.165
–
 2.17
3. 0.507
–
0.51
4. 3.496
–
3.50  3.5
More problems on pg 19
Mrs. Keele, I want to be
a nurse, not a
mathematician! Why do
I have to learn this?
What does this have to
do with nursing?
You are to administer 3 tablets with a dosage
strength of 0.04 mg each. What total dosage are
you giving?
– 3 tablets x 0.04 mg =
3
(0 places to the left)
x 0.04 mg (2 places to the left)
12 mg (2 to the left)  .12 mg  0.12 mg
– 3 tablets x 0.04 mg = 0.12 mg
Tablets are labeled 0.2 mg and you are to give 3 ½
(3.5) tablets. What total dosage is this?
– 3.5 tablets x 0.2 mg =
3.5 (1 place)
x 0.2 mg (1 place)
70 mg (2 places)  .7 mg  0.7 mg
– 3.5 tablets x 0.2 mg = 0.7 mg
You gave 2.5 tablets labeled 0.4 mg each, and the
dosage ordered was 1.2 mg. Was this the correct
dosage?
• 2.5 tablets x 0.4 mg =
2.5
(1 place)
x 0.4 mg (1 place)
100 (2 places)  1.00 mg  1 mg
• 2.5 tablets x 0.4 mg = 1 mg
• Answer the question –
– No this was too little of the medication!