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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