Lesson 4-5Mastering Length Conversions

Length Conversions

Units of Measure for Length
 Metric US Standard millimeter centimeter meter kilometer mm cm m km inch foot yard mile in ft yd mi

Most Common Conversion Factors for Length

 Metric US Standard System Conversion 1000 m per 1 km100 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.

 100 mm per 1 cm or 1 cm per 100 mm 100 cm per 1 m or 1 m per 100 cm 1000 m per 1 km or 1 km per 1000 m

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

 Get the idea? Systematic dimensional analysis (conversion ratios) can save a lot of grief! You can use the same easily remembered conversion factor — 100 cm per 1 m — to convert meters to centimeters or vice versa. You don't have to deal with that old problem of trying to remember whether to multiply or to divide. Simply set up the conversion ratio so it cancels the label for the given amount.

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

Metric-to-Metric 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. Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

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:

• 12 in per 1 ft
• 3 ft per 1 yd
• 5280 ft per 1 mi

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. Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

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.

• 2.54 cm per 1 in

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 2-step conversion:

1. Convert feet to inches using the ratio you know:  2.54 cm/ in
2. 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. Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

0406

 Lesson 4-6Mastering 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.

 In the healthcare profession--especially when talking about medications--the term volume refers to liquid measurements.

Units of Measure for Liquid Volume
 Metric US Standard Apothecary microliter milliliter liter mcm ml L fluid ounce pint quart gallon fl. oz pt qt gal grain 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 pt2 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 vice-versa.

 1000 ml per 1 Lor1 L per 1000 ml

 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:
 1250 ml x 1 L 1 1000 ml
Cancel the labels:
 1250 x 1 L 1 1000
Complete the math:
 1250 x 1 L = 1.25 L 1 1000
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

3-1. Convert 0.15 L to cc.

 0.15 x 1000 cc = 150 cc 1 1

3-2  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. Click the Answer button to see the correct answer to the question. Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

US Volume Conversions

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

 16 fl.oz per pt or 1 pt per 16 fl.oz 2 pt per 1 qt or 1 qt per 2 pt 4 qt per 1 gal or 1 gal per 4 qt

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:
 18 fl. oz x 1 pt 1 16 fl. oz
Cancel the labels:
 18 x 1 pt 1 16
Complete the math:
 18 x 1 pt = 1.13 pt 1 16
Result: 1.13 pt

Examples 5: Converting US Volume Measurements

5-1. Convert 0.1 pint to units of fluid ounces.

 0.1 x 16 fl. oz = 1.6 fl. oz 1 1

5-2. Convert 10 pt to qt.

 10 x 1 qt = 5 qt 1 2

5-3. 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.

5-4. 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.Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

Metric/US Volume Conversions

It is possible to make up all sort of metric-to-US and US-to-metric 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.

 1 fl. oz per 29.6 ml or 29.6 ml per fl. oz

Note

Recall that 1 cc = 1 ml, so you can also put the ratio this way:

 1 fl. oz per 29.6 cc or 29.6 cc per fl. oz

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:
 0.75 fl. oz x 29.6 cc 1 1 fl. oz
Cancel the labels:
 0.75 x 29.6 cc 1 1
Complete the math:
 0.75 x 29.6 cc = 22.2 cc 1 1
Result: 22.2 cc

Examples 7: Converting Between Metric and US Volume Measurements

7-1. 100 ml = _____ fl. oz

 100 x 1 fl. oz = 3.4 fl. oz 1 29.6

7-2. 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 ml--a 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.Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

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:
 5 ml per 1 tsp or 1 tsp per 5 ml 3 tsp per 1 tbs or 1 tbs per 3 tsp 8 fl. oz per c or 1 c per 8 fl. oz

Also remember that units of ml and cc are identical.

Examples 8: Converting Household Volume Measurements

8-1.  The instructions on a bottle of cough medicine call for taking 2 tsp every six hours. How much is each dose in ml?

8-2. How many cubic centimeters in one cup?

Recall that 1 fl. oz = 29.6 cc

8-3. 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.Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

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.Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

0407

 Lesson 4-7Mastering Mass/Weight Conversions

 Metric US Standard Apothecary microgram milligram gram kilogram mcg mg g kg ounce pound ton oz lb T grain 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

 1000 mcg per 1 mg or 1 mg per 1000 mcg 1000 mg per 1 g or 1 g per 1000 mg 1000 g per 1 kg or 1 kg per 1000 g

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

2-1. Convert 0.02 gm to milligrams.

2-2. 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.Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

US Standard Mass (Weight) Conversions

 16 oz per 1 lb or 1 lb per 16 oz 2000 lb per 1 T or 1 T per 2000 lb

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.Click the Next button to see the next question. Your browser does not support inline frames or is currently configured not to display inline frames.

Mixed-Standard Mass Conversions

 1 gr per 60 mg or 60 mg per 1 gr

Examples x: Converting Grains

How many grains in one ounce?

0408

 Lesson 4-8Mastering Time and Rate Conversions

999