# Fraction

MATH MODULE 2.2 Length Measurements Created by Leecy Wise and Caitlyn Reese, Unlimited Learning, Inc. Please use your mouse to click through each slide. That will allow animations and quizzes to play correctly. Move your cursor here to use back arrow 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. 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:

The metric system The English (household) system The apothecary system 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. 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 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 Most people in other countries use the metric system for everything! 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. Thats why it is very important for all health workers to be familiar with the metric system! 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 pounds With 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 heres the good news. You dont have to remember all of that in the metric In the metric system, all measurements differ by 10s: Like tens, hundreds, thousands, ten-thousands and so on AND decimals such as Tenths, hundredths, thousandths, ten-thousandths, etc. 0 10 1 . 0 0.0

00 1 1 0 1 0 0 0 0 0 . 0 0 , 1 10 , 0

1 0 0 0 . 0 PSST! If youre not sure what that means, dont worry! Well explain it in detail later. Okay, now that weve talked about the two main systems of measurement, lets get back to the different units for measuring LENGTH NEXT EXIT 5 MILES Length Length describes an objects size from one end to another;

it may also describe the distance between objects. Here are some examples: I am 5 feet (ft) 7 inches (in.) tall His house is 7.5 miles (mi) from his work The patient has a 2.5 inch (in.) incision on his chest We usually use inches and feet for measuring length in the U.S. But meters (m) are the basic unit for measuring lengths in the metric system. In the English System, we call 3 feet (36 in.) a yard. 1 meter (abbreviated 1 m) is only slightly longer than 1 yard! A yard is 36 inches; a meter is 39 inches.

Yardstick Meter stick If you look at how these two measuring sticks are divided, youll notice that the yard is divided into feet and inches, and the meter stick is divided into centimeters. Notice how much smaller centimeters are compared to inches!!! meter stick yardstick 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 What do you notice about the word centimeter? Perhaps you noticed that its 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 Theres actually A LOT of prefixes that are used in the metric system, that all have meanings very similar to this. Lets looks at another one: DECI- is another Latin prefix that means one tenth

Deci- = 1/10 So, how big is one decimeter? If you said that one decimeter is one tenth of a meter, youre right! 1 centimeter (one hundredth of a meter) 1 decimeter (one tenth of a meter) Notice how decimeters (dm) arent 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). Lets do one more for right now: Milli- is another

Latin prefix that means one thousandth milli- = 1/1000 So, how big is one millimeter? Did you say that one millimeter is one thousandth of a meter? Yes! Youre getting the hang of it now 1 millimeter (one thousandth of a meter) 1 centimeter (one hundredth of a meter) 1 decimeter (one tenth 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. Check your answers. Cross out any wrong answers and correct them on your answer sheet. One meter has decimeters. 10 One meter has centimeters. 100 The abbreviations for the terms you

have now learned are actually easy to remember: 1 meter = 1 m 1 decimeter = 1 dm 1 centimeter = 1 cm 1 millimeter = 1 mm Ask your coach for a metric ruler and draw the following shapes on your Lesson Answer Sheet. Label the measurements of each side. 1. A square with 5 cm sides. 2. An equilateral triangle with 4.5 cm sides.

3. 4. A rectangle with a length of 1 dm and a height of 0.5 dm. A circle with a 50 mm diameter. Ask your coach to check your work when youre done. NOTE: EQUI is a prefix that means SAME. LATERAL means 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 cm But 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 = 1/100 of 1 m th OR 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? Theres 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 1 cm = 100 m Which, if you type 1 100 in the calculator, you will get

0.01 m But do you see a pattern here? Dividing by 100 is the same thing as just moving the decimal point 2 places to the left! 1.0 cm Move the decimal two places . 1.0

Fill in the gaps with zeros .01 m! Now lets look at an example: How would you express 21.6 cm in meters as both a fraction and a decimal? Lets find the decimal form first 21.6 cm Move the decimal two

places . 2 1.6 .216 m Great! Now lets do the fraction form, but wait a minute how do we turn 21.6 cm into a fraction? We cant just put 21.6 over 100! Actually, the easiest way is to use the decimal to help us .216 m This 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: 216 m 1000 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 cm 2) 23 cm 3) 34.6 cm 4) 7.6 cm TIP: Remember that youre 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.

Check your answers. Cross out any wrong answers and correct them on your answer sheet. 1. 13 cm = 0.13 m 13 100 or 24 or 100 2. 24 cm = 0.24 m

3. 346 34.6 cm = 0.346 m or 1000 4. 75 7.5 cm = 0.075 m or 1000 m m m m 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)

This time instead of dividing by 100, were multiplying by 100. This is the same as moving the decimal 2 places to the RIGHT! 1.2 m Move the decimal two places 1.2 . Fill in the

gaps with zeros 120 cm! So, you may have noticed that To go from a smaller to bigger metric unit, we DIVIDE which means we move the decimal LEFT and To go from a bigger to smaller metric unit, we MULTIPLY which so we move the decimal RIGHT X

And guess what else? The decimal trick actually works for ALL metric units!!! 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 To go from dm to m, we are going to a bigger unit, so we move LEFT 30 dm Move the decimal LEFT one place 30.0

3.0 m! *(Then if you needed to go from m to dm, wed be going to a smaller unit, so wed 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 To go from m to mm, we are going to a smaller unit, so we move RIGHT 1.5 m Move the decimal RIGHT three places

1.5 1500 mm *(Then of course to go from mm to m, wed be going to a bigger unit, so wed move LEFT three places) Alright, lets 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. 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) 560 cm to m 2) 4.5 m to dm 3) 1240 mm to m 4) 67 dm to m

Check your answers. Cross out any wrong answers and correct them on your answer sheet. 1) cm to m move 2 places left 560 cm = 5.6 m 2) m to dm move 1 place right 4.5 m = 45 dm 3) mm to m move 3 places left 1240 mm = 1.24 m 4) dm to m move 1 place left 67 dm = 6.7 m THE ENGLISH SYSTEM Also known as the HOUSEHOLD MEASURING SYSTEM Now lets review English

measures used in the U.S for length. Then well learn how to convert back and forth between the metric system and the English System. Youre probably very familiar with the following units of measurement, since in the U.S., we use them everyday: 1 yard (yd) = 3 feet *Note: The yard is the basic unit of length in the English System, which is then divided into smaller units Pretty simple! 1 foot (ft) = 12 inches (in)

The only problem is that when you need to express something smaller than 1 inch, we have to start using fractions (yuck!) Thats one advantage the metric system has. Millimeters are so small that usually fractions arent needed. Now lets try doing some conversions with length units in the English System Keep in mind that when converting between ANY units: 1. When converting from a smaller unit of measurement to a larger one, you divide.

2. When converting from a larger unit measurement to a smaller one, you multiply. x Converting Smaller Units to Bigger Units Lets look at a couple examples: How would you convert 60 inches into feet? Well, since we know there are 12 inches in a foot, and were going from a smaller to a bigger unit, this tells us to divide: 60 in 12 in. per ft = 5 feet

Okay, now lets try converting 27 feet into yards This time we know there are 3 feet in a yard, and again were 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 Converting Bigger Units to Smaller Units Okay, heres a couple more examples to go in the opposite direction: How would you convert 10.5 feet into inches? Here, we still need to know that there are 12 inches in a foot, but were 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 lets try converting 4.5 yards into feet This time we know there are 3 feet in a yard, and again were 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 boys 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 girls length is usually between 2.1 and

Now that you can convert length measurements within both the metric and the household systems, lets convert numbers from one system to another Metric to English and English to Metric Lets 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 divide And to go from yards (bigger) to meters (smaller) you would multiply To go from meters (smaller) to yards (bigger) you would Lets try it. First well 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. Remember: 1 yd = 0.9144 m 6.5 yds = ______ m Were going from bigger to smaller here, so we multiply: 6.5 yds x 0.9144 m per yd = Okay, now try these:

2 yds = ______ m 3.5 yds = ______ m 0.5 m = ______ yds 4.2 m = ______ yds 5.94 m Check your answers. Cross out any wrong answers and correct them on your answer sheet. Multiply or divide depending on whether the units are getting smaller or bigger: 2 yds = 1.83 m 3.5 yds = 3.20 m (2 X 0.9144) (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) Remember, length units in the metric system go down from meters, decimeters, centimeters, then millimeters. So lets look at decimeters and feet next 1 foot = 3.048 decimeters 11Ft Ft 1dm 1dm 1dm 1dm 1dm 1dm

Okay, which one is bigger? Well we can see that a foot is much bigger, a little more than 3 times as long! So divide And to go from feet (bigger) to decimeters (smaller) you would multiply To go from decimeters (smaller) to feet (bigger) you would Okay, ready? Well 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. Remember: 1 ft = 3.048 dm 1.7 ft = ______ dm Were going from bigger to smaller here, so we multiply:

1.7 ft x 3.048 dm per ft = Alright, now try these: 2.5 ft = _____ dm 7 ft = _____ dm 3.2 dm = _____ ft 8.9 dm = _____ ft 5.18 dm Check your answers. Cross out any wrong answers and correct them on your answer sheet. 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) Finally, lets look at converting between inches and centimeters. (There isnt an English measurement that is close in size to millimeters so we dont have to learn any conversions for that) 1 inch = 2.54 centimeters 11inch inch 1cm 1cm 11cm cm Alright, which one is bigger? Well we can see that an inch is a little more than two and half times bigger! So

divide And to go from inches (bigger) to centimeters (smaller) you would multiply To go from centimeters (smaller) to inches (bigger) you would One more time! Well 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. Remember: 1 in. = 2.54 cm 6 in. = ______ cm Were going from bigger to smaller, so we multiply: 6 in. x 2.54 cm per in. = 15.24 cm Alright, now try these: 2 in. = _____ cm 3.6 in. = _____ cm

7.9 cm = _____ in. 8 cm = _____ in. 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. Check your answers. Cross out any wrong answers and correct them on your answer sheet. 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)

Practice problems Round your answers to one decimal point. Write your answers on you Lesson Answer Sheet, then click to check your work. 1. A cafeteria tray measures 1.5 ft long and 1.2 ft wide. Express those dimensions in decimeters. 2. A patients 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.) Check your answers. Cross out any wrong answers and correct them on your answer sheet. 1. The cafeteria tray measures 4.6 dm long by 3.7 dm wide. 2. The patients 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. 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 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? Kilo- is another Latin prefix that means one thousand kilo- = 1000 So, how big is one kilometer? Did you say that a kilometer is equal to 1000 meters? Youre getting it now! So now we know that:

1 kilometer is one thousand meters 1 meter (m) Kilometer (km) 1,000 meters And 1 millimeter is one thousandth of a meter. millimeter (mm) 1/1,000 of a meter 1 meter (m) kilometer (km) 1,000 meters So how many mm do you think are in 1 km?

1000 mm per m x 1000 m per km = 1,000,000 mm per km!!! Review and Practice Turn 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. Dont worry, youll 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-measure ments-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?

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