Download Chapter 1 - Suffolk County Community College

Suffolk County Community College
NUR 103
Fall 2008
• Kathleen Burger, MSEd, MSN, RN, CNE
Assistant Professor of Nursing
MA207 Grant Campus
851-6439
[email protected]
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Medication Errors
• 10-18% of hospital injuries are
attributed to medication errors
• 44,000 to 98,000 people die in U.S.
hospitals annually due to medication
errors
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Basic Mathematics Review
Fractions & Decimals
Textbook Assignment:
Pickar, G. (2007). Dosage calculations: A ratio-proportion approach. (2nd ed.)
Chapter 1
Revised KBurger0808
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Fractions
numerator
denominator
• Math Tip
– Denominator begins with d and is down below
the line in a fraction
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Types of Fractions
• Proper
– Value of numerator is less than value of
denominator
Example:
5
is less than1
8
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Types of Fractions
• Improper
– The value of the improper fraction is greater than
or equal to 1
Example:
8
5 is g reater than 1
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Types of Fractions
• Mixed numbers
– The value of the mixed number is always greater
than 1
Example:
5
1 8 is g reater than 1
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Types of Fractions
• Complex
– The numerator and/or denominator are fractions
• 1/12
1/2
3/4
2
5 1/2
1/4
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Comparing Fractions
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Fractions
• When numerator and denominator are
the same number the fraction is
equivalent to the whole number 1
• 12 = 1
12
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Reducing Fractions
• Divide both terms by the
– Largest nonzero whole number that will divide both
numerator and denominator evenly.
• Value remains the same
6
62
3


10
10  2
5
• Note: 3/5 is an equivalent fraction to 6/10
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Tips for Reducing Fractions
• If the number is even it is divisible by 2
• If the sum of the digits adds up to a
number divisible by 3, the number is
divisible by 3
• If the last digit is 5 or 0, the number is
divisible by 5
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Enlarging Fractions
• Multiply both terms by
– Same nonzero number
• Value remains the same
1
1 2
2


12 12  2 24
Note: 2/24 is an equivalent fraction to 1/12
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Converting Improper Fractions to
Mixed Numbers
• Divide the numerator by the denominator
• Remainders should be written as a proper
fraction in lowest terms
• 13 = 6 1/2
2
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Converting Mixed Numbers to
Improper Fractions
• Multiply the whole number by the
denominator then add the numerator.
• Place that answer as numerator
over the original fractions denominator
• 2 1/6 = [6X2+1] = 13
6
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Adding or
Subtracting Fractions
• Convert to equivalent fractions with
least common denominators
• Add or subtract the numerators
– Place that value in numerator Place least
common denominator as denominator
Convert answer to mixed number
and/or reduce to lowest terms
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Multiply and Divide Fractions
• To multiply
– Cancel terms, multiply numerators, and multiply
denominators
• To divide
- Invert divisor, cancel terms, and multiply
• Convert results to a mixed number
and/or reduce to lowest terms
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Multiplication of Fractions
4
15
5 X 16
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Division of Fractions
 changed to 
1 2 1 7 7
   
4 7 4 2 8
Dividend
Divisor
Inverted
Divisor
Quotient
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Simplification of Complex Fractions
• Complex fractions may be simplified by
performing the indicated division
2/3
5/6 is the same as: 2
3
DIVIDED BY
5
6
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Decimals
WHOLE NUMBERS
DECIMAL POINT
ten thousandths
thousandths
hundredths
tenths
ones
tens
hundreds
thousands
ten thousands
X X X X X . X X X X
DECIMAL FRACTIONS
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Decimals
• 0.001 = one thousandth
• 0.02 = two hundredths
• 0.7 = seven tenths
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Comparing Decimals
• How to compare the following decimals
0.125, 0.05, and 0.2 to find largest decimal fraction
• Align decimal points and add zeros
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Comparing Decimals
0.125 
0.050 
0.200 
125
1, 000
50
1,000
200
1,000
or one hundred twenty-five thousandths
or fifty thousandths
or two hundred thousandths
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Decimal Values:
Decimal Point and Zeros
• To avoid errors the
JCAHO Official DO NOT USE LIST has the
following rules for medication documentation
– Always place a zero to the left of decimal point
Called a leading zero [ 0.5 mg NOT .5 mg ]
– Never place a zero at the of a decimal fraction
Called a trailing zero [ 2.5 mg NOT 2.50 mg ]
– www. JCAHO.org
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Add and Subtract Decimals
• To add or subtract decimals
– Align decimal points and add zeros
– Make all decimals of equal length
– Eliminate unnecessary zeros in final answer
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Multiply and Divide Decimals
• To multiply decimals
– Place decimal point in product to left
– As many decimal places as there are in the two
decimals multiplied
0.25  0.2  0.050  0.05
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Multiply and Divide Decimals
• To divide decimals
– Move decimal point in divisor and dividend the
correct number of decimal places to make divisor
a whole number
– Align it in the quotient
2 0.
1.2 24.0 .
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Multiply and Divide Decimals
• Multiply or divide by a multiplier of 10
– Move decimal point to right (to multiply)
– Move to left (to divide)
– Move number of decimal places as there are zeros in
the multiplier of 10
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Multiply and Divide Decimals
5.06 10  5.0. 6  50.6
2.1  100  .02.1  0.021
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Converting Decimals & Fractions
• Express the decimal number as a whole
number in the numerator of the fraction
• Express the denominator as the number 1
followed by as many zeros as there are
places to the right of the decimal point
• Reduce to lowest terms
• 0.45 = 45/100 = 9/20
• To convert a fraction to a decimal:
Divide the numerator by the denominator
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Rounding Decimals
• Underline the place to which you want to
round
• Look at the value of the number to the right
of this underlined place:
If the number is 5 or greater – round up
If the number is less than 5 – do not change
• Then drop all numbers to the right of the
underlined value
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Thousandths
Hundredths
Tenths
Rounding Decimals

0
.
12
0 .1 2 3

1
.
74
1. 7 4 4
5 . 3 2 5  5.33
0 . 6 6 6  0.67
Rounded to
hundredths
(two places)
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Hundredths
Tenths
0 .1 3
5.6 4
0.7 5
1. 6 6
0.9 5
Rounding Decimals
Rounded to tenths
 0.1
(one place)
 5.6
 0.8
 1.7
 1.0  1
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