Lesson 1 Understanding Percentages 
You see expressions of percentages scattered about in you everyday life as well as at your work as a nurse or other health professional. For instance, "Street crime has increased by 12%", or "Bring a 0.9% saline solution." Just from everyday living and occupational experience, most of us have a fairly good grasp of the meaning of percentages. But that isn't enough for a health professionalwe must also be able to work with percentages on a daytoday basis and create our own statements of amounts, changes in amounts, and percentages.
What does percent mean? One clue is the fact that centum is the Latin word for hundred. So when we say "20 percent," we mean 20 per 100, or 20 out of a hundred.
How much is 25 cents? There's that word again—centum. Twentyfive cents is 25 parts of a hundred cents (a hundred cents is, of course, equal to one dollar).

Topic 1
Notation for Percents
Percents (parts per 100) are most often marked with a percent sign %.
For example, if 40 out of a hundred cars are colored white, you can say that 40 percent (written as 40%) of cars are painted white.Examples

Here are a few everyday examples of expressing partsperhundred with the percent sign:

"Percent solution" is one of the most common expressions of percentage in health and medicine. 
Examples:
Express the following amounts as a percentage
1. 30 items out of 100 Ans: 30%  2. 85 items out of 100 Ans: 85%  3. Two items out of a hundred. Ans: 2% 
Percents can also be expressed as fractions  a percentage value placed over 100.
For example, 12% can be expressed as 12/100
So, writing a percentage as a ratio (fraction) is a simple matter of showing the number of items over 100
Procedure

Percents can be expresses in decimal form  a percentage value times 0.01.
For example, 12% can be expressed as 12 x 0.01
Exercises
Percent Notation These examples help you master the three basic forms of notation for percentages. 
Adjusting Fraction and Decimal Values to % Notation
Most arithmetic operations with percentages are best done using the fraction or decimal forms. Generally speaking, the procedure goes like this:
Note

Exercises
Percent Notation Use these Examples & Exercises to check your understanding and build your confidence when converting fraction and decimal notation back to % notation. 
But what if need to rewrite a fraction with % notation, but the denominator isn't 100? Simply this: Adjust the fraction so that the denominator is 100.
Example
Problem: Rewrite 15/50 with % notation.
Solution: Multiply both the numerator and denominator by a value that forces the denominator to 100. That value would be 2 in this example:
15  x  2  =  30  =30 
50  2  100 
15/50 = 30%
Important

Exercises
Fraction to % Notation Use these Examples & Exercises to check your understanding of how to convert any fraction to the equivalent % notation. 
There is more to the percent number line that integers between 0 and 100. Here is what you will be studying in this section:
Percents that have fraction/decimal parts, such as:
56½%, ¼%, 37.8%, 3.625%
Percents that are greater than 100, such as:
110%, 200%, 102.4%
Percents with Fraction or Decimal Parts
Sometimes you will find percents that include fractions and decimal values. Financial reports and mortgage rates, for instance, sometimes include percentages written as 6½ % or 12.3 %. There is nothing tricky about these fractional parts of a percent. They are simply parts of onehundred percent.
You will also find percentages that are less than 1. Examples are 0.1%, 0.125%, and so on. These are nothing more than expressions of small percentages—amounts that are less than 1 out of 100.
Recall To rewrite a percent to decimal:

Examples
Rewrite 12½ % as a decimal value: 12½ x 0.01 = 12.5 x 0.01 = 0.125
Rewrite ½ % as a decimal value: 12½ x 0.01 = 12.5 x 0.01 = 0.125
Rewrite 44.25% as a decimal value 44.25 x 0.01 = 0.4425
Exercises
Percent to Decimal Use these Examples & Exercises to check your understanding of how to rewrite percents with fraction parts to decimal. 
Of course, you should also be able to rewrite any fraction or decimal value to percent.
Recall To rewrite a decimal or fraction to percent:

Examples
Rewrite 0.0625 as a percent: 0.0625 x 100 = 6.25% or 6¼%
Rewrite 0.005 as a percent: 0.005 x 100 = 0.5% or ½%
Rewrite 0.00021 as a percent: 0.0002 x 100 = 0.021%
Rewrite 1/8 as a percent: 1/8 x 100 = 100/8 = 12.5%
Exercises
Decimal to Percent Use these Examples & Exercises to check your understanding of how to rewrite any decimal/fraction to percent. 
Procedure To rewrite a percent to decimal:

Examples
Rewrite 12½ % as a decimal value: 12½ x 0.01 = 12.5 x 0.01 = 0.125
Rewrite ½ % as a decimal value: 12½ x 0.01 = 12.5 x 0.01 = 0.125
Rewrite 44.25% as a decimal value 44.25 x 0.01 = 0.4425
Exercises
Percent to Decimal Use these Examples & Exercises to check your understanding of how to rewrite percents with fraction parts to decimal. 
Of course, you should also be able to rewrite any fraction or decimal value to percent.
Procedure To rewrite a decimal or fraction to percent:

Examples
Rewrite 0.0625 as a percent: 0.0625 x 100 = 6.25% or 6¼%
Rewrite 0.005 as a percent: 0.005 x 100 = 0.5% or ½%
Rewrite 0.00021 as a percent: 0.0002 x 100 = 0.021%
Rewrite 1/8 as a percent: 1/8 x 100 = 100/8 = 12.5%
Exercises
Decimal to Percent Use these Examples & Exercises to check your understanding of how to rewrite any decimal/fraction to percent. 
Percents Less than 1
More Examples
Express the following amounts as a percentage
1. 30 items out of 100 Ans: 30%  2. 85 items out of 100 Ans: 85%  3. Two items out of a hundred. Ans: 2% 
Topic 2
Fractions, Decimals, and Percents
Percents indicate the amount per 100. So any percentage can be rewritten as a fraction that has 100 as its denominator:
percent =  number or amount 
100 
Procedure

Examples
1. Rewrite 57% as a fraction.
Place the 57 over 100: 7% =
57 100
2. Rewrite 40% as a fraction
Place the 40 over 100: 40% =
40 100
Reduce the fraction: 40 , =
2 100 5
3. Rewrite 61½% as a fraction.
This procedure requires an extra step and the understanding that dividing any number by 100 is the same as multiplying it by 1/100.
Convert 61½ to an improper fraction: 61½ =
63 2
Divide by 100 (multiply by 1/100): 63 x
1 =
63 2 100 200
4. Rewrite 110% as a fraction.
Place the 110 over 100: 110
100
Reduce the fraction: 110 =
11 1000 10
Rewrite the improper fraction as a mixed number: 11 = 1
1 10 10
Exercises
Rewrite percents as fractions
Now let's turn around the operation and rewrite a fraction as a percent.
The basic idea is to convert the two terms of the fraction such that the denominator is equal to 100. For example, rewrite 6/10 as a percent. First you multiply the numerator and denominator by 10. This gives you the necessary value of 100 in the denominator. Finally, remove the denominator and attach the % sign to the remaining value (what had been the numerator).
6 =
6 x 10 = 60 10 10 10 100
60 , = 60%
100
Procedure

Examples
1. Rewrite  1  as a percent. 
4 
Multiply the numerator and denominator by a value that forces the denominator to 100:
1 x
25 = 25 4 25 100
Rewrite 25 as a percent.
100
25 , = 25%
100
Exercises
Rewrite fractions as percents
Converting between decimal values and percents is much simpler than conversions with fractions.l
Procedures

Examples
1. Rewrite 30% as a decimal value
Drop the percent sign: 30% → 30
Divide by 100: 30 ¸ 100 = 0.30
30% = 0.3
2. Rewrite ½% as a decimal value
Drop the percent sign: ½% → ½
In this example: rewrite the fraction as a decimal value: ½ = 0.5
Divide by 100: 0.5 ¸ 100 = 0.005
½% = 0/005
3. Rewrite 0.65 as a percent
Multiply by 100: 0.65 x 100 = 65
Attach the percent sign: 65%
4. Rewrite 0.001 as a percent
Multiply by 100: 0.001 x 100 = 0.1
Attach the percent sign:0.1%
Exercises
Rewrite fractions as decimals and decimals as fractions
40% can be rewritten as 40/100, but such fractions ought to be reduced. So:
40% = 40/100 = 2/5.
Examples
You have seen how a given percent can be rewritten as a fraction. It is sometimes necessary to turn that process around and convert a given fractional amount to a percentage. Here is an easy example:
11/100 = 11%
This was an easy example because the denominator was already 100. Now let's work with a fraction that does not have 100 as a denominator. The procedure, in this case, requires you to convert the fraction so that it DOES have a denominator of 100. Then simply rewrite in as a percent. See the following example.
Example
P
Topic 3
Working with Percents
There are three terms common to all percentage problems:
In this expression, 5% of 40 = 2
5% is the percentage (P)
40 is the base (b)
2 is the amount of difference (a)
Percentage problems generally fall into three categories:
1. Find percentage of change, given the base and amount of change.
Example: What number is 6% of 50?
2. Find the amount of change when the percentage and base are known.
Example: 20 is what percent of 60?
3. Find the base when the percentage and amount of change are known.
The number 5 is 25% of what number?
Procedure

Find the percentage of change when an original amount and new amount are known
A typical verbal problem of this type goes something like this: A certain item in the store normally sells for $60. It is now on sale with a 15% discount. What is the amount of discount? What is the sale price?
The amount of discount is found by calculating 15% of the normal selling price:
Amount of discount is 15% of $60: 0.15 x $60 = $9
The sale price is found by subtracting the amount of discount from the normal selling price:
Sale price = $60  $9 = $51
A variation of the same kind of problem concerns an independent Web designer who finds she has to increase her rate by 12%. If the current rate is $80 per hour, how much will the hourly rate increase? What is the new hourly rate?
The amount of increase is found by calculating 12% of the current rate.
Amount of increase is 12% of $80: 0.12 x $80 = $9.60
The new rate is then found by adding the amount of increase to the current hourly rate:
New rate = $80 + $9.60 = $89.60
Over a period of time, the amount of liquid in a vial drops from 120ml to 50ml. What is the percent of decrease?
The amount of decrease is found by subtracting the lower amount from the original:
Amount of decrease = 120ml  50ml = 70ml
The percent of decrease is found by taking
The percent of decrease is 70/120 x 100 = 58.3%
, what is the new rate?
The amount of increase
Exercises
A certain amount is what percent of another amount?
Topic 4
Percent of Increase or Decrease
The percent of change (increase or decreases) is an indication of how much a quantity changes.

Examples
1. An original amount of 25 units undergoes an increase of 2 units. Determine the percent of change.
Percent Change =
2 x 100% = 8% 25
2. A vial containing 500 units of a liquid is reduced by 100 units. Determine the percent of change.
Percent Change =
100 x 100% = 20% 500
3. An item in a store is marked down 14%. Determine the sale price if the item normally sells for $45.00.
Percent Change =  1  x 100%  
25 
Example
0402
Lesson 2 Understanding Ratio and Proportion 
0403
Lesson 3 Introduction to Measurement Standards 
The Metric System of Measurement
Linear Measurements
Linear measurements are measurements of distance. (Linear = Linelike).
The main unit of distance in the metric system is the meter. Think of 1meter as being the distance you would normally find between the center of a doorknob and the bottom of the door, or the floor. All the other labels for distances in the metric system are based on that one particular distance. Here are some multiples you should know:

The standard distance from a doorknob to the floor is approximately 1 meter. 
Volume Measurements
In medical practice, volume measurements refer specifically to liquid volume. And in the metric system, the basic unit of liquid volume is the liter. A standard wine bottle holds 3/4 of a liter. In the US system of measurement, a liter is essentially the same as a quart. A subdivision of the liter is the milliliter:
You will also see occasional references to the cubic centimeter (cc). The 1 cc is exactly equal to 1 ml.

A standard wine bottle holds 3/4 of a liter. 
Mass Measurements
The terms mass and weight are often used interchangeably. Technically speaking, they mean different things; however, only physicists and engineers will obsess over the differences. The basic unit of mass in the metric system is the gram (gm). A standardsize metal paperclip weighs close to 1 gm.
 A ripe pineapple weighs about one kilogram 
The US Standard System of Measurement
The US Standard system of measurement is built around units of feet, fluid ounces, and pounds.
US Linear Measurements

US Volume Measurements
The units of volume in the US system are:


US Weight Measurements


The Household System of Measurement
The household system of measurement includes all the common (and many notsocommon) measurements found throughout traditional kitchen recipe books. Only three household measures have any significance for health care:


The Apothecary System of Measurement
Like the household system of measurement, the apothecary system has a relatively large number of units. The relationships between the units are often complicated and curious. Fortunately, there is only apothecary label still in common use for general health care: the grain.
grain — gr
0404
Lesson 44 Working with Dimensional Analysis 
The term dimensional analysis sounds more like something you might find in rocket science than medicine. However, dimensional analysis is actually a simple, but powerful idea. It is simple because it always takes the same form: a series of two or more ratios that are multiplied together. It is powerful because it virtually eliminates the need for recalling large numbers of measurement conversions and formulas. Master the basic idea of dimensional analysis, and you no longer have to ask, " Do I multiply or divide to make this conversion or calculate this dosage?" 
Dimensional analysis is NOT rocket science. 
Relative Amounts and Ratios
Recall that a ratio expresses the relative value of two amounts. "Two out of three, " for example, can be expressed as the ratio 2/3. "One in a hundred" can be expressed as 1/100.
Now consider the fact that there are 16 fl. oz in a pint. That can also be expressed as a ratio: . That is saying "Sixteen fluid ounces per one pint." It's a ratio that happens to include labels as well as numerical values.
You know that there are 100 cm in a meter. This can be expressed in two ways:
says there are 100 centimeters in a meter.
says there is 1 meter per 100 centimeters.
Both are correct. Both say the same thing. The ratios are equal.
The success of dimensional analysis depends your knowing:

Examples 1:
Express each of the following conversions as two ratios.
Known Conversion Ratios There are 12 inches in one foot
12 in 1 ft
1 ft 12 in There are 1000 ml in a L
1000 ml 1 L
1 L 1000 ml 16 oz = 1 lb
16 oz 1 lb
1 lb 16 oz You can substitute 3 teaspoons of medicine for one tablespoon.
3 tsp 1 tbs
1 tbs 3 tsp
You know it is not unusual to have medications mixed with sterile water. The concentration of the medication can then be expressed as mg of medication per ml of fluid. So if there is 10 mg of medication in 100 ml mixture, the concentration can be expressed as:
Expressing Relative Amounts as a Pair of Ratios
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

Setting Up Ratios to "Cancel" Labels
When you first studied rations and proportions, you found that you can "cancel" equal terms in order to simplify the multiplication of fractions or ratios.
Example
Given:
5 x
3 8 5
Cancel "crosswise" terms that are equal
5x 3 = 1 x 3 8 58 1 Complete the multiplication
1 x 3 = 3 8 1 8
For the purposes of dimensional analysis, you can also "cancel" labels:
Explanation
In the first step, you are simply setting up a product of two ratios you should know: there are 100 mm in 1 cm, and there are 10 cm in 1 m.
100 mm x
10 cm 1 cm 1 m In the second step, notice that cm appears in the denominator of one term and in the numerator of the other term. This means you can "cancel" the cm labels — not the numerical values, but the labels, themselves.
100 mm x
10 cm1 cm1 m The third step simply shows the product of the two ratios, having cancelled out the common labels (cm, in this example)
100 mm x
10 1 1 m And finally, you complete the multiplication of the numerical terms, sliding the remaining labels over into the final ratio.
100 mm x 10 = 1000 mm 1 1 m 1 m The final result says that there are 1000 mm in one meter. And of course that is true.
Example 2:
Use a product of ratios (dimensional analysis) to convert 575 milligrams to grams.
The given amount is 575 mg. Expressing this as a ratio:
You should know that the conversion ratio for milligrams and grams is
Set up those two ratios for multiplication:
Strike out labels that can be cancelled:
Complete the multiplication:
Answer: 575 mg is equal to 0.575 g
"Cancelling Labels" and Completing the Multipication
The ratios have been set up for you in this drill. Your job is to complete the task by cancelling labels are appropriate and doing the multiplication. Click the Answer button to see the correct answer to the question. 

Important The whole trick to dimensional analysis is to set up the ratios in such a way that all the labels you don't want in the final result are "cancelled." 
Example 3
Convert 1500 mg to grams.
The given ratio is and you want the result to be in grams. So you need a conversion ratio for converting between milligrams and grams.
The conversion ratios you can choose from are and . These ratios are equal. They are both used for converting between units of milligrams and grams. The big question is this: which one do you use in our example — for converting 1500 mg to grams?
Let's try the analysis using the conversion ratio, .
The trouble with using this form of the conversion ratio is that none of the labels cancel. So It must be the wrong choice.
So try the other version, ,and see what happens:
Now the mg labels cancel, leaving the answer in grams.
1500 mg is equal to 1.5 g.
Example 4
Convert 0.2 pounds to ounces.
The given ratio is:
The conversion ratios for pounds and ounces are and
Which one should you use for converting the given ratio to units of ounces?
Try doing the analysis with the first conversion ratio:
You can see that the pound (lb) labels will cancel, leaving on the oz label for the answer. So that is the correct choice:
Try the other conversion ratio, , and you will see that nothing can be cancelled.
Ans: 0.2 lb = 3.2 oz.
Choosing Conversion Ratios
Select the ratio that allows you to cancel all unwanted labels, leaving only the label(s) required for the final answer. Click the Answer button to see the correct answer to the question. 

The Structure of Dimensional Analysis
The most convincing reason for using dimensional analysis is simplicity. Every conversion problem and every dosage calculation look exactly the same way — products of ratios. And there are just three basic kinds of ratios:
The Given Ratio is the one that shows the information given by the problem. If you are required to convert 122 inches to feet, for example, the given amount is 126 in, and given ratio is .
The Conversion Ratio is the one that contains the necessary conversion numbers and labels. When converting between inches and feet, the correct conversion ratio is .
The Result Ratio is the product of the given ratio and conversion ratio: . (The Result Ratio should be simplified to a single term when you have finished the work. In this example, should be simplified as 10.5 ft).
There can be only one Given Ratio and One Result Ratio, but there can be more than one Conversion Ratio. This happens when there is more than one unit conversion involved in the problem.
Here is an example of a dimensional analysis that uses two conversion ratios to complete the job. Don't panic over the complicatedlooking equation. Just identify the parts and note that each one says something you probably understand rather well. In this example, you convert a speed expressed in meters per second into a speed expressed in kilometers per hour. Such problems usually get people all anxious about which to multiply or divide my which. Dimensional analysis, however, orders everything. 
Example 5
Convert 2000 meters per second into kilometers per hour.
The Given Ratio is
One of the conversion ratios has to deal with seconds and hours: or
The second conversion ratio works with meters and kilometers: or
The dimensional analysis look like this:
Note how the conversion ratios are selected so that the meters and seconds cancel, leaving just the desired kilometer and hour.
0405
Lesson 45 Mastering Length Conversions 
Length Conversions
Metric  US Standard  




Most Common Conversion Factors for Length
Metric  US Standard  System Conversion 
1000 m per 1 km 100 cm per 1 m 1000 mm per 1 m  12 in per 1 ft 3 ft per 1 yd 5280 ft per 1 mi  2.54 cm per 1 in 1.61 km per 1 mi 
Length Conversion Map
Metric Length Conversions
Metric length conversions are relatively easy because the conversion factors are all multiples of 10. You don't need the aid of a calculator because all the calculations are simply multiplying or dividing by multiples of 10.



Example 1: Converting meters to centimeters
Convert 0.12 m to cm.
Given Length: 0.12 m Conversion Factor: 100 cm/m  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 120 cm 
Example 2: Converting centimeters to meters
Convert 1500 cm to m.
Given Length: 1500 cm Conversion Factor: 1 m/100 cm  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 1.5 m 
Example 3: Converting meters to kilometers
Convert 16500 m to km
Given Length: 16500 m Conversion Factor: 1 km/1000 m  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 16.5 km 
Example 4: Converting centimeters to millimeters
Convert 0.175 cm to mm
Given Length: 0.175 cm Conversion Factor: 100 mm/1 cm  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 17.5 mm 
MetrictoMetric Conversion Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

US Standard Length Conversions
US Standard conversions are a bit more difficult than metric conversions, mainly because the conversion factors are not simple multiples of 10:
So a calculator can be helpful at times for making conversions that include any US Standard lengths.
NOTE Leave answers in decimal form. All but the US building trades use decimal forms of US Standard lengths. For example, cite 1.25 ft instead of 1 ft 3 in., and 1.5 inches instead of 1½ ". 
Example 5: Converting Inches to Feet
Convert 44 in to ft.
Given Length: 44 in Conversion Factor: 1 ft/12 in  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 3.67 ft 
Example 6: Converting Yards to Feet
Convert 1.25 yd in to ft.
Given Length: 1.25 yd Conversion Factor: 3 ft/1 yd  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 3.75 ft 
US Standard Conversion Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

Converting Between Metric and US Standard Lengths
Here is the only conversion ratio you must be able to recall. You can use dimensional analysis with two conversion factors to work with any other combination of metric and US terms.
Example 7: Converting Centimeters to Inches
Convert 43 centimeters to inches
Given Length: 43 cm Conversion Factor: 2.54 cm/in  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 16.93 in 
Example 8: Converting feet to centimeters
How many centimeters are in 1 foot?
If you don't happen to recall the number of centimeters in a foot, you can use a 2step conversion:
 Convert feet to inches using the ratio you know: 2.54 cm/ in
 Convert that result to feet using another ratio you know: 12 in/ft
Given Length: 1 ft Conversion Factors: 12 in/ft, 2.54 cm/in  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 30.5 cm 
Example 9: Converting miles to kilometers
How many miles are in 4 kilometers?
Make this a special challenge by assuming you do not recall the number of kilometers in one mile. All you can recall is: 2.54 cm/1 in, 12 in/1 mi, and 5280 ft/mi.
Given Length: 4 km Conversion Factors: 1000 m/km, 100 cm/m, 1 in/2.54 cm, 1 ft/12 in, 1 mi/5280 ft  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 2.49 mi 
Example 10: Converting millimeters to inches
Convert 150 mm to inches.
Given Length: 150 mm Conversion Factors: 2.54 cm/in, 10 mm/cm  
Set up Given Length and Conversion Factor 1:  
Attach Conversion Factor 2:  
Cancel the labels:  
Complete the math:  
Result: 0.59 in 
Ans: 150 mm is 0.59 in
Metric/US Standard Conversion Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

0406
Lesson 46 Mastering Volume Conversions 
Volume is the measure of the amount of space an object or substance occupies. A grain of sand has a minuscule volume compared with the Rock of Gibraltar; nevertheless, the lowly grain of sand has a measurable volume. Solids, liquids, and gasses that are confined to some sort of container, all occupy space and can be measured in terms of their volume.

Metric  US Standard  Apothecary  




 gr 
NOTES: You will occasionally see liquid volume expressed in units of cubic centimeters (cc). This isn't a cause for concern, however, because 1 cc is the same as 1 ml. As a health professional, you won't work with microliters (mcm) very often. Science and technology professions prefer the label mL. The US Standard ounce is properly called a fluid ounce (fl. oz) to distinguish it from the weight/mass version where 16 ounces (oz) equals one pound (lb). 
Most Common Conversion Factors for Liquid Volume  
Metric  US Standard  System Conversion 
1,000,000 mcm per L 1000 ml per L  16 fl.oz per pt 2 pt per qt 4 qt per gal  1 qt = 0.946 L 
Volume Conversion Map
Metric Volume Conversions
Metric volume conversions are relatively easy because the conversion factors are all multiples of 10. In fact, there is only one purely metric volume conversion: milliliters to liters and viceversa.

Note: The cubic centimeter (cc) measurement is still used today, but you should easily remember that 1 cc is equivalent to 1 ml. 
Example 1: Converting Milliliters to Liters
Convert 1250 ml to L
Given Volume: 1250 ml Conversion Factor: 1 L per 1000 ml  
Set up the ratios: 
 
Cancel the labels: 
 
Complete the math: 
 
Result: 1.25 L 
Example 2: Converting Liters to Milliliters
Convert 0.055 L to ml
0.055 L
x
1000 ml 1 1 L
0.055
x
1000 ml 1 1
0.055
x
1000 ml = 55 ml 1 1 0.055 L = 55 ml
Note Notice how you don't have to figure out whether your are supposed to multiply or divide. You simply take the proper conversion factor ( 1000 ml per 1 L, in these examples) and arrange it so the unwanted labels cancel out. In Example 1, you want to get rid of the ml label, so you flip over the conversion ratio so that the ml label is on the bottom. In Example 2, you want to get rid of the L label, so you flip over the same conversion factor so that L labels cancel. 
Examples 3: Converting Between Liters and Cubic Centimeters
31. Convert 0.15 L to cc.
0.15
x
1000 cc = 150 cc 1 1 32 1280 cc = _____ L
1280
x
1 L
= 1.28 L 1 1000
Metric Volume Drill
Work with this drill routine until you can consistently make the conversions correctly.


US Volume Conversions
The US Standard volume measurements most commonly encountered in the healthcare professions are:



Example 4: Converting Fluid Ounces to Pints
Convert 18 fl. oz to pt
Given Volume: 18 fl. oz Conversion Factor: 1 pt per 16 fl. oz  
Set up the ratios: 
 
Cancel the labels: 
 
Complete the math: 
 
Result: 1.13 pt 
Examples 5: Converting US Volume Measurements
51. Convert 0.1 pint to units of fluid ounces.
0.1
x
16 fl. oz = 1.6 fl. oz 1 1 52. Convert 10 pt to qt.
10
x
1 qt = 5 qt 1 2 53. Convert 0.1 gallon to quarts.
0.1
x
4 qt = 0.4 qt 1 1 Sometimes you have to use multiple conversion ratios, rather that looking up conversion factors you haven't memorized.
54. Convert 1600 fluid ounces to gallons.
US Standard Volume Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

Metric/US Volume Conversions
It is possible to make up all sort of metrictoUS and UStometric volume conversions, but there is just one that stands out from the rest: converting between cc (or ml) and fluid ounces. In fact, if you memorize this conversion ratio you will be able to use multiple conversion ratios to work out any other metric/US volume conversion without having to memorize or look up their ratios.
 Note Recall that 1 cc = 1 ml, so you can also put the ratio this way:

Example 6: Converting Fluid Ounces to Cubic Centimeters
Convert 3/4 fl. oz to cc
Given Volume: 0.75 fl. oz Conversion Factor: 29.6 cc per fl. oz  
Set up the ratios: 
 
Cancel the labels: 
 
Complete the math: 
 
Result: 22.2 cc 
Examples 7: Converting Between Metric and US Volume Measurements
71. 100 ml = _____ fl. oz
100
x
1 fl. oz = 3.4 fl. oz 1 29.6
72. 1 L = _____ fl. oz
The conversion ratio for liters and fluid ounces is not ordinarily provided on conversion charts. So it is necessary to convert the liter to another unit that is normally associated with fluid ounces ... and that would be ml. You should know by now that 1 L = 1000 ml, so substitute that ratio:
So instead of trying to work with liters
1
x
1 fl. oz = 1 ??? work with the equivalent number of mla conversion ratio that is more commonly known:
1000
x
1 fl. oz = 33.8 fl. oz 1 29.6 Answer: 1 L = 33.8 fl. oz
Fluid Ounces and Cubic Centimeter Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

Household Volume Measurements
The household volume measurements you are likely to encounter as a health worker are cup (c) , teaspoon (tsp or t), and tablespoon (tbs or T). Here are the conversion ratios:
Also remember that units of ml and cc are identical. 
Examples 8: Converting Household Volume Measurements
81. The instructions on a bottle of cough medicine call for taking 2 tsp every six hours. How much is each dose in ml?
82. How many cubic centimeters in one cup?
Recall that 1 fl. oz = 29.6 cc
83. 1 tbs = _____ ml
Household Measurements Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

Topic Summary: Volume Conversions
Volume Conversions Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

0407
Lesson 47 Mastering Mass/Weight Conversions 
Metric  US Standard  Apothecary  




 gr 
Note The label for micrograms (mcg) is used primarily in medicine and pharmacy. It is written as mg in most technical trades and science professions. 
Mass (Weight) Conversion Map
Metric Mass Conversions



Example 1: Converting Micrograms to Milligrams
Convert 3500 micrograms to milligrams.
Given Mass: 3500 mcg Conversion Factor: 1000 mcg per 1 mg  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 3.5 mg 
Examples 2: Converting Metric Mass
21. Convert 0.02 gm to milligrams.
22. Express 5 mg in micrograms.
Volume Conversions Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

US Standard Mass (Weight) Conversions


Example 3. Converting Pounds to Ounces
Convert 35 oz to pounds
Given Mass: 35 oz Conversion Factor: 1 lb per 16 oz  
Set up the ratios:  
Cancel the labels:  
Complete the math:  
Result: 2.19 lb 
Mass Conversions Drill
Work with this drill routine until you can consistently make the conversions correctly. Click the Answer button to see the correct answer to the question. 

MixedStandard Mass Conversions

Examples x: Converting Grains
How many grains in one ounce?
0408
Lesson 48 Mastering Time and Rate Conversions 
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