 The Science Notebook
Exploring Measurement - Length

MEASURING THINGS

People have measured things for thousands of years.  We have always wanted to know, “How much?”, “How long?”, “How far?”, or “How tall?”  the science of measuring answers those questions, and in the process, it helps us to describe things in a more exact way.

For example, suppose you are describing your two cousins to a friend. You say that one cousin is taller than the other. Your friend asks, “How much taller?”, and you say “A lot!”  Then she says, “Well, how much is a lot?”

When you try to describe how tall each cousin is without using numbers, you have a very difficult time of it.  However, by measuring, you can use numbers and units of measurement that will give your friend a much better idea just how tall each cousin is. You might tell your friend that one cousin is 150 cm (4 ft 7 in) tall, and the other is 15 cm (6 in) taller.  Now your friend will have a much better idea of just how tall each of your cousins is. Using units of measurement like centimeters or inches makes it much easier to get the idea across.

Scientists constantly measure things when they do experiments.  If a scientist is studying how a particular type of plant is affected by heat or cold, it isn’t enough to say that the air around one plant was hot and around the other was cold.  The temperature around each plant must be measured.  Neither is it enough to say one plant is bigger than the other one.  The scientist will have to measure the plants to see just how much bigger. And what does “bigger” mean?  Measurements such as the height of each plant, its weight, the size of the leaves, or other characteristics, help to describe how one plant is bigger than another.

In these experiments on the Measurement pages, we will explore some ways things may be measured, and what these measurements mean.  As we do, we will be making some devices that will be very useful for measuring and doing other experiments throughout this site.

We will also compare the system of measurement used in the United States, known as the “English system”, with the measurement system used by most other countries and by nearly all scientists, which is called the “metric system”.  We’ll see how each one came to be and why scientists prefer to use the metric system instead of the English one.

Exploring Length - English Style

How tall are you?  How long is a football field?  How far is it to your school?  How far is the earth from the sun?  How big is that little paramecium you saw under the microscope in science class?  All of these questions ask how long something is, but the answer in each case is very different.  If you live in the United States, you probably measure your height in feet and inches, the length of the football field in yards, the distance to your school in miles, the distance from the earth to the sun in millions of miles, and the size of that paramecium in thousandths of an inch.  But, did you ever wonder where all those units - inches, feet, yards, and miles - came from?  Let’s find out.

Materials Needed:  Ruler; yardstick, or tape measure; several volunteer friends.

Procedure:   For each volunteer, measure and record the following in inches:  the length of the nose from the forehead to the tip; the length of the bottom of the foot; and the distance from the tip of the nose to the end of the index fingertip of an outstretched arm. Put the measurements in a table like this:

 Name Nose (in) Foot (in) Nose to Fingertip (in) Joe C. 1 ¾ 10 ½ 33 Donita Z. 1 ½ 9 28

What To Look For: Did you measure any nose that was exactly one inch?  Any foot that was exactly 12 inches?  How about any nose tip to finger tip that was exactly 36 inches?

What Happened: No one knows for sure how feet, inches or yards came about, but many believe that they came from the lengths of various body parts.   One theory says that these lengths were set by the length of these body parts of the king or queen in power at the time.  Thus, the length of the royal nose became the standard for one inch, the length of the royal foot became the standard for one foot, and the distance from the tip of the royal nose to the tip of the royal index finger became the standard for one yard.  As you can see from your measurements above, the length of each of these could vary greatly depending on who was king or queen at the time.  People apparently got tired of changing these lengths each time a new king or queen came along, and at some point, the lengths for each of these units became standard throughout the British Empire.

Going Further: There are many different units of length in the English system of measurement.  Look at a table of English weights and measures in a math book, almanac, dictionary or encyclopedia.  Some will be very familiar, some you may have heard of but may not be familiar with, and some you’ve probably never heard of at all.  How would you like to have to keep up with all of them?

Walk a Mile in Your Shoes

Materials Needed: A good pair of walking shoes; a watch; a safe place to walk a mile.

Procedure: Find a location such as a school track that has a measured mile.  Time how long it takes you to walk one mile and record the time.

Using that time, figure out how long it would take you to walk the following distances:

 Across the United States 2,500 miles From the Earth to the Moon 250,000 miles From the Earth to the Sun 93,000,000 miles

You may need to get an older student, adult or teacher to help you do the math, since you will have to convert minutes to hours, days, and even years.

What To Look For: A very slow mile will take about fifteen minutes to walk.  You will probably do it in much shorter time.

What Happened: Assuming a 15 minute mile, it would take you the following times (approximately) to walk the above distances:

 Across the United States 2,500 miles 26 days* From the Earth to the Moon 250,000 miles 7.1 years* From the Earth to the Sun 93,000,000 miles 2654 years*

*This is walking nonstop for twenty four hours a day - no time to eat or sleep!

One mile is equal to 5,280 feet.  Here’s how that distance came about.  English measurement for a length of land was a unit called the rod, which was an old Saxon unit. A rod equals 5.5 yards (16.5 feet).   40 rods equals one furlong, which was traditionally the length of a row on old English farms. In 1592, the length of a mile was set at 8 furlongs, which works out to 1760 yards or 5280 feet.  Confusing, isn’t it?

Exploring Length - Metric Style

The English system of measurement served its purpose, and in many respects, is still a useful system today.  Those of us who live in the United States eventually learn the most common conversions for most of the everyday measurements - inches, feet, yards and miles. In fact, because this is the system man of us first learned, it seems very natural to use these units.  However, most of us never bother with rods, furlongs, fathoms, leagues or other English units used to measure length simply because we don’t need them.

But the problem with the English system is that there are so many different units, and these units can get confusing after a while.  Also, if you have to convert even lengths you are familiar with - say, inches to yards - you have to remember conversion factors from one unit to another, and there are several to remember.  Also, many of the conversions don’t seem to be related to one another at all.

In the 1790's, the French decided to do something about this.  They developed a system of measurement called the Metric System.  The units in the metric system are much simpler to work with because there is only one basic unit for each quantity being measured. To measure length, all of the English units you have looked at have been replaced by just one unit - the meter. Let’s look closely at a meter, and we’ll see why it is such a good unit to measure things.

Materials Needed: Meter stick; yard stick.

Procedure:   You can probably borrow a meter stick from your school.  Place the meter stick beside the yard stick.  Which is longer?  By about how many inches?  (By the way, some yard sticks also have metric divisions on the reverse side, and some meter sticks inches on the reverse. Does yours?)

What To Look For: You will notice that the meter is just a bit longer than the yard, a little over three inches, in fact.  This is the basic unit of measurement in the metric system for length. And as we will see elsewhere in the Measurement pages, the meter is also used to define the basic units of weight and volume.

The length of the meter was originally based on the distance from the North Pole to the equator, or one quarter of the distance around the earth.  The meter was defined as - are you ready for this? - one ten millionth of that distance! Today, the length is defined very differently, but the actual length of the meter is still the same.

Anything that can be measured in yards can also easily be measured in meters, since the two lengths are about the same.  You only need to remember that a meter is a little longer than a yard.

Going Further:   But what about things that can’t be easily measured in yards?  Can we use the meter to measure things we usually measure in inches, feet or miles?  As it turns out, we can, and we can do it without having to do all those conversions that are required in the English system! CAUTION!  Always use sharp objects such as knives or scissors with adult supervision only!  Hold any sharp point away from your body, particularly your eyes.

In this experiment, you will make your own meter stick. As you do, you will see how the meter is divided into smaller units.  If you work carefully, you will have a meter stick that you can use in other investigations.

Materials Needed: Meter stick; thin strip of wood at least one meter long.  (If you don’t have a thin strip of wood, you can use a thin strip of cardboard.); scissors or hobby knife; ruler or straight edge; pen or pencil.

Procedure:     Place the meter stick on top of the strip.  If the strip is longer than a meter, use your straight edge to draw a line at exactly one meter.  Have an adult to help you cut the wood strip off at this line so that you have a strip that is exactly one meter. Examine the meter stick you are using carefully.  You will notice that it is divided into ten equal parts.  Look for the longest dividing lines on the meter stick.  (There will be nine of them.)  Make marks on the wood strips at each of these lines, and carefully draw in your own dividing lines at each of these marks.  Try to make the lines all the same length.

Each of the units you just marked is 1/10 of a meter.  1/10 of a meter is a ”decimeter.”  The prefix “deci-” means 1/10, so there are ten decimeters in a meter.  Count them.

Now look at one decimeter on your meter stick.  Notice that each decimeter is also divided into ten equal parts.  Each of these parts is called a “centimeter”.  A meter is divided into a hundred decimeters, so each centimeter is 1/100 of a meter.  The prefix “centi-” means 1/100.  It will take a little while, but mark off the centimeters on your meter stick.  The marks for each centimeter should be the same length, and these marks should be shorter than the decimeter marks.  Also note that there will be nine of these marks between the decimeter marks.

Take one more look at the meter stick.  Look for the shortest dividing lines. These small lines divide the meter stick into 1000 equal parts.  Each part is 1/1000 of a meter and we call each part a “millimeter”.   The prefix “milli-” means 1/1000.

You do not need to mark each millimeter on your stick, but you can if you want to be able to measure more accurately.

What Happened:  The trick to using a meter stick to measure shorter lengths is dividing it into smaller units, and it really isn’t a trick at all.  The meter is divided by tens to get all of the units we need to measure.  These divided measurements are identified by prefixes which tell you what part of a meter they are.  So far, you have learned three of the four you will need to know - deci- (one tenth), centi-.(one hundredth), and milli- (one thousandth). There is another bit of good news about these prefixes.  They are the same ones used throughout metric system.  You won’t have to learn a lot more!

Using the Meter to Measure Shorter Lengths

The meter stick described above may be used to measure many lengths that you would normally use feet or inches to measure.  Measuring lengths in the metric system is actually very easy, but it takes a little practice.

Materials Needed: Meter stick (the homemade meter stick described above will work just fine); ruler; Post-it Notes ®  (or similar); a friend.

Procedure:  Stand up against a wall and have a friend hold a ruler over your head to mark your height.  Mark this spot on the wall with a Post-it paper.  Now mark your friend’s height the same way.

Using your meter stick, measure both your height and your friend’s height in centimeters. If you aren’t sure how to use the meter stick to measure centimeters, you may want to ask an older student or teacher to help you.

What To Look For:  In countries that use the metric system, a person’s height is generally measured in centimeters. Many lengths shorter than a meter are measured in centimeters as well.

What Happened: Depending on how tall you are, your height is probably somewhere between 100 and 200 centimeters.   The centimeter is a convenient unit for things you would normally measure in inches. You may have wondered why the decimeter isn’t used.  It could be, but for most lengths, centimeters are used instead.

Going Further: Once you understand how to measure in centimeters, you should practice measuring different objects around your home or classroom until you’re sure you know how to do it.

Measuring Much Smaller Lengths Using the Meter

Centimeters are fine for measuring most lengths up to a few meters, but if we want to measure smaller objects, and measure them accurately, we need to use those little tiny marks on the meter stick - the millimeters.

Materials Needed: A ruler that is divided into metric units, or a meter stick; several small objects to measure (each should be less than 6 inches long).

Procedure: Many plastic and school rulers are divided into metric units as well as inches. You probably have such a ruler in your house or at school.  If you examine it closely, you will notice that the metric side is divided into centimeters, and that each centimeter is further divided into ten equal parts.  Each of these parts is one millimeter.  If you don’t have such a ruler, you can always use a meter stick that is divided into millimeters, although it may be a little harder to handle.

Use the meter stick to measure the objects you selected in millimeters.

What To Look For: The millimeters will have marks but they won’t be numbered, so you’ll have to remember that there are ten millimeters in a centimeter.  For example, if the object you’re measuring is a little over five centimeters, to the five centimeter mark will be fifty millimeters.  Then you count the individual marks from there to the end of your object and add that number to fifty to get the total number of centimeters.

If you have trouble understanding this, get an older student or teacher to show you how it is done.

What Happened: A six inch object is almost 152 millimeters.  You may have wondered why we would want to use such tiny measurements.  The answer is simple.  When measuring small objects such as the ones you just did, the millimeter is much more accurate than inches, and the good news is that you don’t have to worry about all those different fractions of an inch.

Going Further: Once you understand how to measure in millimeters, continue to practice measuring objects until you are confident you know how to do it well.

Measuring Much Larger Lengths Using the Meter

You have seen how you can use the meter, decimeter, centimeter, and millimeter to measure lengths.  These may easily replace yards, feet and inches.  But what about long distances measured in miles in the English system?  We can use the meter to measure those distances, too.

Materials Needed: Meter stick; (the homemade meter stick described above will work just fine); calculator.

Procedure:  This experiment is really a “thought” experiment, because you are going to do it in your mind.  Look at your meter stick again.  Remember, it is a little longer than a yard.  A football field is 100 yards long, so if you were to add a little bit to that length, it would be 100 meters long.

Imagine a distance ten times as long as that football field plus a little more.  That would be 10 times 100 meters or 1000 meters.  1000 meters is is the unit we use to measure longer distances in the metric system.  1000 meters is called a “kilometer”.  The prefix “kilo-” is our fourth and final prefix, and it means 1000.

A kilometer is approximately equal to 3/5 (.6) mile, so you can see it is just a little more than half as long as a mile.  Trying to think in terms of kilometers instead of miles is probably the hardest part of working with metric lengths, because, unlike the meter and the yard, the two lengths aren’t all that similar.

The only way to “practice” using kilometers is to convert familiar distances in miles to kilometers.   To convert miles to kilometers, multiply the miles by 3/5 (or .6).  Use a calculator, if necessary.  Complete the following table:

 Distance Miles Kilometers Across the United States 2,500 ? From the Earth to the Moon 250,000 ? From the Earth to the Sun 93,000,000 ? From your home to your school ? ? From your home to _____ ? ?

Going Further: Let’s review what you need to remember about measuring length in the metric system.

1.  It’s all based on the meter.
2.  A meter is just a little longer than a yard.
3.  All the other units we need are made by dividing or multiplying the meter by tens.
4.  The other units are identified by adding prefixes.  The “big four” are:

Prefix     Means
Kilo-        1000
Deci-       1/10  (or .1)
Centi-      1/100  (or .01)
Milli-       1/1000  (or .001)

These are the same prefixes that are used in measuring volume and weight.

Understanding how to measure length is a good start, but measurement is so important in science that you should check out our page on Measuring Volume.  After that, check out our page on Measuring Mass.

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