The metric system

Scientific data is always reported using metric system units of measurement. There are four basic metric measurement units:

• Length = meter (m)

• Volume = liter (l)

• Mass (weight) = gram (g)

• Temperature = ° Celsius (° C )

All four metric system basic units can be converted into larger or smaller units simply by adding a prefix in front of the basic unit:

Unit prefixes:

• kilo (k) = Makes the basic unit 1000 times larger (103)

• centi (c) = Makes the basic unit 100 times smaller (10-2 or 1/100)

• milli (m) = Makes the basic unit 1000 times smaller (10-3 or 1/1000)

• micro (µ) = Makes the basic unit a million times smaller (10-6 or 1/1,000,000)

For example, a person might weigh 63,000 grams. That same person also weighs 63 kilograms since each kilogram is equal to 1000 grams. These larger and smaller units are called “derived” units.

A note on the letter abbreviations of the metric system: When you see a single letter being used as an abbreviation for a unit, the single letter always represents one of the four basic metric units. For example, the letter m by itself stands for meter, the letter L by itself stands for liter, the letter g by itself stands for gram, and the letter C by itself stands for degree Celsius. But

when you see two letters being used as an abbreviation for a unit, the first letter always represents a derived unit prefix and the second letter always represents a basic unit. Here are some examples of two letter abbreviations: km = kilometer, kg = kilogram, cm = centimeter, mg = milligram, mm = millimeter, µg = microgram, µL = microliter.

One of the skills that you should learn from today's lab is to be able to convert between basic units and derived units in the metric system. Here is an example problem that requires conversion of metric units:

230 centimeters = __________ meters

Your first step in doing a metric conversion problem is to focus on the units (not the number) of the problem. The units are being converted from centimeters to meters. Because meters are 100X larger than centimeters, the units in this problem are becoming 100X larger. This is step shown below:

The second step in a conversion problem focuses on the number (not the units). The number must change in the opposite way as the units changed. In this problem, the units became 100X larger. Therefore, the number in the problem must become 100X smaller. This step is shown below:

As practice, try to use the same two-step method to solve the following problem:

0.98 liters = ___________ milliliters.

If you used the two step method correctly, you should have obtained an answer of 980 milliliters.

In some metric conversion problems, there is a derived unit on both sides of the problem. An example of such a problem is the one below:

548 centimeters = _________ millimeters

In problems like the one above, it is best to break the problem into two parts. The first part is to convert the starting value into the basic metric unit. In example problem this would be:

548 centimeters = 5.48 meters.

The second part is to convert the basic unit value into the answer units that the problem asks for:

5.48 meters = 5480 millimeters.

In today’s exercise you will become familiar with metric system units and converting between large and small metric units. In each of the sections that follow, you will first familiarize yourself with the appropriate metric unit until you have a “feel” for its size, then you will estimate the measurements of some everyday objects. Finally, you will measure the objects to see how close your estimates were. The answers to these measurements are given at the end of this handout.

A) Length

The basic unit of length in the metric system is the meter (m). Common derived units are the centimeter (cm) (10-2 or 1/100 of a meter) and the millimeter (mm) (10-3 or 1/1000 of a meter). For measuring large distances, the kilometer (103 or 1000 meters) is often used.

Obtain a wooden meter stick (1 meter in length). As you can see by looking at the meter stick (and from the picture below) a meter is close to one yard in length.

Also obtain plastic metric ruler. Most rulers in the United States show inches and centimeters. For example, on the ruler in the photo below the numbered lines at the top of the ruler show inches but the numbered lines at the bottom of the ruler show centimeters.

The numbered graduations (graduations means lines) on the bottom of the ruler are 1 centimeter apart. But if you look closely you will see that each centimeter is divided into 10 smaller graduations. For example, there are 10 tiny graduations between the number 5 line and the number 6 line on the bottom of the ruler. Those smallest graduations on the metric ruler are millimeters. In summary, there are 10 millimeters per one centimeter.

As a lab group, spend a few minutes looking at the meter stick and the ruler. Try to memorize how big a meter is, how big a centimeter is, and how big a millimeter is. Here are a few metric length "guideposts" to help you:

* A meter is almost the same length as a yard (3 feet)

* A penny is almost exactly 2 centimeters wide. So 1 centimeter is about half a penny's width.

* A credit card is about 1 millimeter in depth. A dime is also about 1 millimeter in depth.

Now, as a group, get up and estimate the lengths of the following objects in metric units. After each length estimation, compare your estimation to the actual value. You can find the actual length by measuring the object yourself or by looking at the answers at the bottom of this handout.

Object: Estimate:

1) Width of door (meters) ________ m

2) Height of door (meters) ________ m

3) Length of a dollar bill (centimeters) ________ cm

4) Length of a fork (centimeters) ________ cm

5) How far apart are the tines of a fork? ________ mm

6) Width of your pinkie's fingernail (centimeters) ________ cm

7) Depth of a smart phone (in millimeters) ________ mm

B) VolumeThe basic unit of volume in the metric system is the liter (l). The most common derived unit is the milliliter (ml) (10-3 or 1/1000 of a liter). The volume of a milliliter is equal to the volume of a cube 1 centimeter per side. Another derived unit is the micrometer (µl) (10-6 or 1/1,000,000 of a liter).

A familiar example of a liquid that is measured in liters is soft drinks. Grocery stores sell soft drinks in 2 liter bottles. So if one of these soft drink bottles were cut in exactly in half it could contain exactly 1 liter volume of soft drink.

A teaspoon is about 5 milliliters volume. So a teaspoon that is 1/5 full is holding about 1 ml volume of liquid.

Another way to think of a milliliter volume is that it is roughly 20 drops of water.

As a lab group, spend a few minutes looking at the 1 liter of bottle of water (in half filled soda bottle) and the 1 ml plastic cube. Try to memorize how big a liter is, how big a milliliter is. Here are a few metric volume "guideposts" to help you:

* A gallon milk jug holds about 4 liters.

* A large soft drink bottle holds 2 liters of liquid.

* A 12 ounce soda can holds about 350 ml.

* A standard coffee mug holds about 300 ml of liquid.

When you are doing the volume estimations, how do you measure the actual volumes of the objects you have estimated?

• To measure the volume of a liquid, it is usually poured into a beaker or cylinder with measurement marks (or “graduations” as they are sometimes called). The top of the liquid forms a slight curve, called a “meniscus”. The volume of the liquid is the graduation closest to the bottom of the meniscus. For example, the liquid in the graduated cylinder below has a volume of 53 ml.

• The volume of solid objects (like rocks, for example) can be obtained by measuring how much water they displace in a beaker or graduated cylinder. To measure the volume of an object using this method, first partially fill a beaker or graduated cylinder with water. Record the volume of water. Next, submerge the object completely under the water. The increase in the water’s volume is equal to the object’s volume. Hint: Use as small a beaker as possible for your object. The smaller the beaker, the more accurate your measurement will be.

• Very small volumes of water can be accurately measured using a scale, because each milliliter of water weighs 1 gram. To measure water this way, first put a small beaker on the scale, “zero” the scale by pressing the tare button (O/T on our scale). Be sure the readout shows a little “g” after the zero. If it says “N” the reading is not in grams. Now add the water to the beaker Each gram that the scale reads equals 1 ml of water.

Now estimate the volumes of the liquids and objects listed below. It helps to hold the 1 ml cube or the liter bottle next to the object while estimating its volume. After you have recorded each volume estimate, compare your estimation to the actual value. You can find the actual volume by measuring the object yourself or by looking at the answers at the bottom of this handout.

Object: Estimate:

1) Water in a standard toilet tank ________ l

2) Water in typical full bathtub ________ l

3) Water in full tablespoon of water ________ ml

4) Volume of a tennis ball ________ ml

5) Volume of a typical brick ________ ml

C) Mass (weight)

The basic unit of mass in the metric system is the gram (g). The most common derived unit is the milligram (mg) (10-3 or 1/1000 of a gram). For measuring large masses, the kilogram (103 or 1000 grams) is often used.

Obtain the box of metric weights from the counter. As a lab group, spend a few minutes holding the various weights in your hand to get a feel for a kilogram, 500g, 200g, 1g etc. Try to memorize the feel of a weight of a kilogram, 500 grams, 200 grams, 100 grams, and a gram. Here are a few metric mass "guideposts" to help you:

* A regular paper clip or a thumbtack both weigh about 1 gram.

* A wooden pencil weighs about 7 grams.

* An egg weighs about 50 grams.

* A can of Coca Cola weighs about 400 grams (it would weigh 360 grams if it had no sugar but the sugar adds about 40 grams to its mass).

* A 1 liter bottle of water weighs 1 kilogram.

Masses are measured by using a scale (which is also called a balance). Before you weigh anything on a balance, first place a container to hold the object (for example, a beaker to hold water if you are weighing water or a pan if you are weighing a solid). Next, press the tare button (labeled O/T on

our scale) to reset the balance to zero. The balance may take a moment to zero itself. (The zero should have a “g” after it for grams). Lastly, place the object in the container and read its weight.

If the mass of an object and the volume of the object are both known, the density of the object can be calculated. The formula for density is simply the object’s mass (in grams) divided by its volume (in ml). For example, a 76 gram piece of gold might have a volume of 4 milliliters. The density of gold is therefore:

(76 grams) / (4 milliliters) = 19 grams per milliliter

Estimate the masses of the objects below. After you have recorded each mass estimate, compare your estimation to the actual value. You can find the actual mass by measuring it on a balance or by looking at the answers at the bottom of this handout.

Object: Estimate:

1) Nickel (grams) ________ g

2) Penny (grams) ________ g

3) Your own mass (kg) ________ kg

4) A typical brick (kg) ________ kg

5) What is the density in grams per milliliter (g/ml) of a typical brick? (Section B must be completed to answer this question).

Density of typical brick = _______________ g/ml

Would the density of the brick be different if you had used a larger piece of the same brick? _________________

D) Temperature

The basic unit of temperature in the metric system is the degree Celsius. (° C ). There are no commonly derived units.

To get a feel for degrees Celsius, consider the following temperatures "guideposts::

* Ice water and the freezing point of water are 0 ° C

* Room temperature and tap water are 20 – 25 ° C

* Normal body temperature is 37 ° C

* Water gets too painful to touch between 50 – 60 ° C

* Water boils at 100 ° C

With the above temperatures in mind, estimate the temperatures of the following four liquids. After you have recorded each temperature estimate, compare your estimation to the actual value. You can find the actual temperature by measuring it on a thermometer or by looking at the answers at the bottom of this handout.

Object: Estimate:

1) Milk in a typical refrigerator ________ ° C

2) Water coming out of the cold sink faucet ________ ° C

3) Water coming out of the hot sink faucet ________ ° C

4) Ice water ________ ° C

Review questions

Convert the following values into the new units. Use the unit factor method and show all your work.

1) 8 meters = ______ mm

2) 22.1 ml = _______ l

3) 10,900 cm = _______ m

4) 0.0034 mg = _______ g

5) 0.0087 l = ________ µl

6) 660 g = _______ mg

7) 0.98 kg = _______ g

8) 0.00003 m = _______ mm

9) 57 mm = ________ cm

10) 0.98 kg = ______ mg

11) 349 ml = __________ µl

12) 4590 µl = _______ ml

13) How many grams does 73 ml of pure water weigh?

14) What is the volume of 0.23 kg of pure water?

15) Pure gold has a density of 19 g/ml. If you bought a “gold” ring and found it had a volume of 0.3 ml and that it weighed 5.7 grams, is it real gold?