MATH MODULE 2.2

Distance Measurements:

Length, width, depth, and heightCreated by Leecy Wise and Caitlyn Reese, © Unlimited Learning, Inc.

2015

Please use your mouse to click through each slide. That will allow animations and quizzes to play correctly.

Use the back arrow key on your keyboard or the back arrow icon at the bottom left part of each slide to move to previous slides.

Move your cursor here to use back arrow

Measuring is part of our everyday life. We measure ingredients for recipes, distances to places, minutes, miles per gallon, weight, and more.

Measuring is also an essential part of all medical and scientific professions.

The most common categories of measuring that are used in healthcare are length, weight, volume, time and temperature.

Nurses and other health professionals use three systems of measurement in their work:

These sound complicated, but they are actually easy to use with practice.

In this module we will discuss the two most commonly used systems, and then you will learn how to convert amounts from one system to another.

• The metric system

• The English (household) system• The apothecary system

In this module we will cover the metric system and the English system.

The Apothecary system is probably the oldest drug

measurement system, and it is sometimes still used today. This system uses Roman numerals and terms like

grains, drams, and minims. We will not cover the apothecary system

here. You might come across it later in your health career, but the metric and English

systems are used much more often.

THE METRIC SYSTEM

That’s why it is very important for all health workers to be familiar with the metric system!

In the United States, we tend to use the English system for daily purchases and household use (like pounds, cups, and inches), but that is not the case in most of the world…

In fact, the metric system is also called the SI system, which means the International System of Units. This

system is used across the world so that scientists from different countries can exchange information easily,

without having to worry about converting between different units.

So, to make sure medical information can also be communicated easily with the rest of the world, healthcare workers in the U.S. almost always use the metric system for patient measurements and drug dosages.

Most people in other countries use the metric system for everything!

But how do you measure in the metric system? You are probably used to:

• Yards, feet, and inches

• Gallons, quarts, and cups

• Tablespoons and teaspoons

• Ounces and poundsWith this system you have to constantly remember that 1 cup has 8 liquid ounces and that 1 pound weighs the same as 16 ounces, and so on…

Well here’s the good news. You don’t have to remember all of that in the metric

system!

In the metric system, all measurements differ by 10’s:

10

0.010.10

0.000110,000

0.001 1001,000

• Like tens, hundreds, thousands, ten-thousands and so on… AND decimals such as…

• Tenths, hundredths, thousandths, ten-thousandths, etc.

PSST! If you’re not sure what that means, don’t worry! We’ll explain it in detail later.

Okay, now that we’ve talked about the two main systems of measurement, let’s get back

to the different units for measuring

LENGTHNEXT EXIT

5 MILES

Length describes an object’s size from one end to another; it may also describe the distance between objects.

Length

Here are some examples:

I am 5 feet (ft) 7 inches (in.) tall

His house is 7.5 miles (mi) from his workThe patient has a 2.5 inch (in.) incision on his chest

But meters (m) are the basic unit for measuring lengths in the metric system.

Meter stick

We usually use inches and feet for measuring length in the U.S.

In the English System, we call 3 feet a yard.

Well, 1 meter (abbreviated 1 m) is very close to 1 yard! In fact, a yard is only about 3 inches longer than a meter:

Yardstick

If you look at how these two measuring sticks are divided, you’ll notice that the yard is divided into feet and inches,

and the meter stick is divided into centimeters.

And of course you probably know that each

foot has 12 inches…

But you may not know that each meter has 100 centimeters.

There is no unit within a meter that has a length similar to feet. Usually lengths are

either measured in whole meters or centimeters, but nothing in between.

1 meter =

100 cm

meter stick

yardstick

Notice how much smaller centimeters

are compared to inches!!!

What do you notice about the word

centimeter?Perhaps you noticed that it’s simply the word “meter” with “centi-” attached to the front.

Actually, those two word parts give us the exact meaning of the whole word, and can help us remember exactly how big a centimeter is!

CENTI- is actually something called a prefix that comes from Latin (a prefix is a word part that you attach to a larger word part to change the meaning).

Centi- means “one hundredth,” so when we attach it to the word “meter” it translates to “One hundredth of a meter”

Centi- = 1/100

“DECI-” is another Latin

prefix that means one tenth

There’s actually A LOT of prefixes that are used in the metric system, that all have meanings very similar to this. Let’s looks at another one:

Deci- = 1/10

So, how big is one decimeter?

If you said that one decimeter is one tenth of a meter,

you’re right!

1 decimeter (one tenth of a meter)

1 centimeter (one hundredth of a meter)

Notice how decimeters (dm) aren’t separately marked on metric rulers; all you see is the marking for 10 cm. In general, most things are simply measured in meters (m) or centimeters (cm).

“Milli-” is another Latin prefix that

means one thousandth

Let’s do one more for right now:

milli- = 1/1000

So, how big is one millimeter?

Did you say that one millimeter is one thousandth of a meter? Yes! You’re getting

the hang of it now…

1 decimeter (one tenth of a meter)

1 centimeter (one hundredth of a meter)1 millimeter (one thousandth of a meter)

Okay, now test your knowledge!

Write the answers for the blanks on your Lesson Answer Sheet. Click to check your answers.

One meter has ________ decimeters.One meter has ________centimeters.One meter has ________millimeters.

One meter has 10 decimeters.

One meter has 100 centimeters.

One meter has 1000 millimeters.

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

The abbreviations for the terms you have now learned are actually easy to remember:

1 meter = 1 m1 decimeter = 1 dm1 centimeter = 1 cm1 millimeter = 1 mm

1. A square with 5 cm sides.2. An equilateral triangle with 4.5 cm sides. 3. A rectangle with a length of 1 dm and a

height of 0.5 dm.4. A circle with a 50 mm diameter.

Ask your coach to check your work when you’re done.

NOTE: EQUI is a prefix that means SAME. LATERAL means side.

Ask your coach for a metric ruler and draw the following shapes on your Lesson Answer Sheet. Label the measurements of each side.

Now that you know how the metric system works to measure length or height, you will need to know how to convert between units of the metric system.The good news is that you have already learned about tenths, hundredths and thousandths in the metric system.

Now we know that one meter has one hundred centimeters:

1 m = 100 cmBut how do we express centimeters in terms of meters?Actually, there are two ways:

Like you saw before, we can express 1 cm as a fraction of one meter…

1 cm = 1/100th of 1 mOR

We can express 1 cm as a decimal in meters…

1 cm = 0.01 m This is the hundredths place. So, by putting a 1 in this spot, we are saying “One hundredth,” just like the fraction!

Alright, so are you ready for a secret?

There’s actually a really easy way to turn centimeters into meters as a decimal…

To go from centimeters to meters, you basically are dividing by 100, right?

1.0 cm

= 1100 m

Which, if you type 1 ÷ 100 in the calculator, you will get…

0.01 mBut do you see a pattern here?

Dividing by 100 is the same thing as just moving the decimal point 2

places to the left!

Move the

decimal

two places

1.0Fill in the

gaps

with zeros

. .01 m!

1 cm

Now let’s look at an example: How would you express 21.6 cm in meters as both a fraction and a decimal?

21.6 cm 2 1.6. .216 m

Let’s find the decimal form first… Move

the decimal

two places

Great! Now let’s do the fraction form, but wait a minute… how do we turn 21.6 cm into a fraction? We can’t just put 21.6 over 100!

Actually, the easiest way is to use the decimal to help us…

.216 mThis decimal goes all the

way out to the thousandths place

This is the same as saying we have two-hundred and sixteen

thousandths of a meter

As a fraction, this is written:

2161000 m

Now you try it! Express the following centimeter amounts in meters, as a fraction AND as a decimal. Write your answers on your Lesson Answer Sheet, then click to check your answers.

1) 13 cm2) 23 cm3) 34.6 cm4) 7.6 cm

TIP: Remember that you’re dividing by 100, so you can move the point over to the left two places to get the decimal form. Then you can use the decimal form to help you get the fraction if needed.

1. 13 cm = 0.13 m or m

2. 24 cm = 0.24 m or m

3. 34.6 cm = 0.346 m or m

4. 7.5 cm = 0.075 m or m

10013

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

Guess what? The decimal trick actually works in both directions!

Say that this time you wanted to go from meters to centimeters (the opposite of before)…

1.2 mThis time instead of

dividing by 100, we’re multiplying by 100. This is the same as

moving the decimal 2 places to the RIGHT!

Move the

decimal

two places

1.2Fill in the

gaps

with zeros

. 120 cm!

To go from a smaller to bigger metric unit, we DIVIDE which means we move the decimal LEFT

and

So, you may have noticed that…

÷

To go from a bigger to smaller metric unit, we MULTIPLY which so we move the decimal RIGHT

X

How about if you wanted to convert between meters and decimeters?

The only difference is that instead of dividing or multiplying by 100, you would use 10, and only move 1 decimal place. For example…

And guess what else? The decimal trick actually works for ALL metric units!!!

30 dmMove the decimal

LEFT one place

30.0 3.0 m!To go from dm to m,

we are going to a bigger unit, so we

move LEFT

*(Then if you needed to go from m to dm, we’d be going to a smaller unit, so we’d move RIGHT one place)

And finally if you wanted to convert between meters and millimeters…

You would be dividing or multiplying by 1000, and you move 3 decimal places! For example…

1.5 mMove the decimal

RIGHT three places

1.5 1500 To go from m to mm,

we are going to a smaller unit, so we

move RIGHT

mm

*(Then of course to go from mm to m, we’d be going to a bigger unit, so we’d move LEFT three places)

Alright, let’s try it.Do the following conversions within the metric system

using our decimal trick. Write your answers on your Lesson Answer Sheet, then click to check your work.

1) 560 cm to m2) 4.5 m to dm3) 1240 mm to m4) 67 dm to m

Remember: • Small to big is DIVIDE which means the decimal moves LEFT• Big to small is MULTIPLY which means the decimal moves RIGHT• But you have to figure out HOW MANY places the decimal moves

1) cm to m move 2 places left560 cm = 5.6 m

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

2) m to dm move 1 place right4.5 m = 45 dm

3) mm to m move 3 places left1240 mm = 1.24 m

4) dm to m move 1 place left67 dm = 6.7 m

Now let’s review English measures used in the U.S

for length. Then we’ll learn how to convert back and forth between the metric system and the English

System.

THE ENGLISH SYSTEM Also known as the

HOUSEHOLD MEASURING SYSTEM

1 yard (yd) = 3 feet

You’re probably very familiar with the following units of measurement, since in the U.S., we use them everyday:

1 foot (ft) = 12 inches (in)Pretty simple!

The only problem is that when you need to express something smaller than 1

inch, we have to start using fractions (yuck!)

That’s one advantage the metric system has.

Millimeters are so small that usually fractions aren’t

needed.

*Note: The yard is the basic unit of length in the English

System, which is then divided into smaller units

1. When converting from a smaller unit of measurement to a larger one, you divide.

Now let’s try doing some conversions with length units in the English System…

÷Keep in mind that when converting between ANY units:

x2. When converting from a larger unit measurement to a smaller one, you multiply.

How would you convert 60 inches into feet?

Converting Smaller Units to Bigger Units Let’s look at a couple examples:

Well, since we know there are 12 inches in a foot, and we’re going from a smaller to a bigger unit, this tells us to divide:

60 in ÷ 12 in. per ft = 5 feet

Okay, now let’s try converting 27 feet into yards…This time we know there are 3 feet in a yard, and again we’re going from a smaller

to a bigger unit, so this tells us to divide here as well:

27 ft ÷ 3 ft per yard = 9 yards

How would you convert 10.5 feet into inches?

Converting Bigger Units to Smaller Units Okay, here are a couple more examples to go in the opposite direction:

Here, we still need to know that there are 12 inches in a foot, but we’re going from a bigger to a smaller unit, so this time we need to multiply:

10.5 ft x 12 in. per ft = 126 in

Okay, now let’s try converting 4.5 yards into feet…This time we know there are 3 feet in a yard, and again we’re going from a bigger to

a smaller unit, so this tells us to multiply here as well:

4.5 yd x 3 ft per yard = 13.5 feet*Which is the same as 13 feet

and 6 inches, right?

Okay, your turn!Do the following conversions, and write your answers on your Lesson Answer Sheet. Then click to check your work.

1) A boy’s length at birth is normally between 19.1 and 20.1 inches. Convert this to feet. Round your answers to

one decimal point.

2) At six months, a girl’s length is usually between 2.1 and 2.2 feet. Convert this to inches. Round your

answers to one decimal point.

3) 9 year old boys and girls both tend to have an average height of about 52.5 inches. Convert this to yards. Round your answer to one decimal point.

(Hint: You’ll need to convert to feet first, then convert feet to yards.)

1) A boy’s length at birth is normally

between 1.6 and 1.7 feet

2) At six months, a girl’s length is usually

between 25.2 and 26.4 inches

3) 9 year old boys and girls both tend to have an average height of about

1.5 yards

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

Now that you can convert length measurements within both the

metric and the household systems, let’s convert numbers from one

system to another…Metric to English

andEnglish to Metric

Let’s start with converting between yards and meters…

1 yard = 0.9144 meters Meter stick

Yardstick

First of all, which one is bigger? Well it looks like the yardstick is bigger, plus the amount in meters is a decimal. So…

To go from meters (smaller) to yards (bigger) you would divideAnd to go from yards (bigger) to meters (smaller) you would multiply

Let’s try it. First we’ll give you an example, but try the rest on your own. Round to two decimal places. Write your answers on

your Lesson Answer Sheet, then click to check your work.

2 yds = ______ m

3.5 yds = ______ m

0.5 m = ______ yds

4.2 m = ______ yds

6.5 yds = ______ m

Remember: 1 yd = 0.9144 m

We’re going from bigger to smaller here, so we multiply:

6.5 yds x 0.9144 m per yd = 5.94 mOkay, now try these:

Multiply or divide depending on whether the units are getting

smaller or bigger:

2 yds = 1.83 m (2 X 0.9144)3.5 yds = 3.20 m (3.5 X 0.9144) 0.5 m = 0.55 yds (0.5 ÷ 0.9144) 4.2 m = 4.59 yds (4.2 ÷ 0.9144)

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

1 foot = 3.048 decimeters

Okay, which one is bigger? Well we can see that a foot is much bigger, a little more than 3 times as long! So…

To go from decimeters (smaller) to feet (bigger) you would divideAnd to go from feet (bigger) to decimeters (smaller) you would multiply

Remember, length units in the metric system go down from meters, decimeters, centimeters, then millimeters.

So let’s look at decimeters and feet next…

1 Ft

1dm 1dm 1dm

Okay, ready? We’ll give you an example again, then try the rest on your own. Round to the two decimal places. Write your

answers on your Lesson Answer Sheet, then click to check your work.

2.5 ft = _____ dm

7 ft = _____ dm

3.2 dm = _____ ft

8.9 dm = _____ ft

1.7 ft = ______ dm

Remember: 1 ft = 3.048 dm

We’re going from bigger to smaller here, so we multiply:

1.7 ft x 3.048 dm per ft = 5.18 dmAlright, now try these:

Multiply or divide depending on whether the units are getting smaller

or bigger:

2.5 ft = 76.20 dm (2.5 X 3.048)

7 ft = 213.36 dm (7 X 3.048)3.2 dm = 1.04 ft (3.2 ÷ 3.048)8.9 dm = 2.69 ft (8.9 ÷ 3.048)

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

1 inch = 2.54 centimeters

Alright, which one is bigger? Well we can see that an inch is a little more than two and half times bigger! So…

To go from centimeters (smaller) to inches (bigger) you would divideAnd to go from inches (bigger) to centimeters (smaller) you would multiply

Finally, let’s look at converting between inches and centimeters.

(There isn’t an English measurement that is close in size to millimeters so we don’t have to learn any conversions for that…)

1 inch

1cm 1 cm

One more time! We’ll give you an example, then try the rest on your own. Round to the two decimal places. Write your answers

on your Lesson Answer Sheet, then click to check your work.

2 in. = _____ cm 3.6 in. = _____ cm7.9 cm = _____ in. 8 cm = _____ in.

6 in. = ______ cm

Remember: 1 in. = 2.54 cm

We’re going from bigger to smaller, so we multiply:

6 in. x 2.54 cm per in. = 15.24 cmAlright, now try these:

Notice that the abbreviation for inch (in.) uses a period.

This is the only abbreviation that has a period, to avoid

confusion with the word “in.”

Multiply or divide depending on whether the units are getting smaller

or bigger:

2 in. = 5.08 cm (2 X 2.54) 3.6 in. = 9.14 cm (3.6 X 2.54)7.9 cm = 3.11 in. (7.9 ÷ 2.54)

8 cm = 3.15 in. (8 ÷ 2.54)

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

1. A cafeteria tray measures 1.5 ft long and 1.2 ft wide. Express those dimensions in decimeters.

2. A patient’s bed mattress is 203 cm long by 99 cm wide. Express those dimensions in inches.

3. Mrs. Abudi walked 36.6 dm the day after her surgery. Express that distance in feet.

4. Manuela is 5 ft 4 in tall. Express that height in cm. (Hint: first convert ft to in., and then convert to cm.)

Practice problemsRound your answers to one decimal point. Write your answers on you Lesson

Answer Sheet, then click to check your work.

1. The cafeteria tray measures 4.6 dm long by 3.7 dm wide.

2. The patient’s bed mattress is 79.9 in. long by 39 in. wide.

3. Mrs. Abudi walked 12 feet the day after her surgery.

4. Manuela is 162.6 cm tall.

Check your answers. Cross out any wrong answers and correct them on your answer sheet.

One final word on metric measurements for length and distance. You have practiced using the meter as the basic unit for measuring smaller

distances.If you were not working strictly in the

medical field, you would use the kilometer as your basic measuring unit

for longer distances.

One kilometer (km) is a little more than a mile and a half:

1km = 1.60934 mi

“Kilo-” is another Latin prefix that

means one thousandkilo- = 1000

Drivers in other parts of the world define driving speed in km per hour

(kph), not miles per hour (mph)!

Did you notice a new prefix too?

So, how big is one kilometer?

And 1 millimeter is one thousandth of a meter.

1 meter (m) Kilometer (km)1,000 meters

Did you say that a kilometer is equal to 1000 meters? You’re getting it now!

1 kilometer is one thousand meters…So now we know that:

1 meter (m) kilometer (km)1,000 meters

millimeter (mm)1/1,000 of a meter

1000 mm per m x 1000 m per km = 1,000,000 mm per km!!! So how many mm do you think are in 1 km?

Review and PracticeTurn in your first answer sheet to your coach. Then complete the following worksheets (you should have a print out of them):

Metric Unit Conversion English Unit Conversion Converting between Metric and English Units

Once you complete each worksheet, ask your coach for the answer key and correct your work. Don’t worry, you’ll only be graded for completion on this part.

Finally, click here to review some flash cards with all of the terms you learned in this lesson (you can also play games with the terms!):https://quizlet.com/100185097/math-module-22-length-measurements-flash-cards/

CONGRATULATIONS!You now have a good introduction to length

measurement in the metric and English systems, and how to do

conversions

Ready to take the quiz?