Subject Area Lessons

## #8. The Metric System

Science, level: senior
Posted by Mike Edmondson (medmond@hotmail.com).
Related sites: Teachers.Net Reference Desk - Currency/Unit Convertors
Hardaway High School
Materials Required: I have some graphics that go with this that I can e-mail direct to you - rulers, cylinders - that sort of thing.
Activity Time: 1 week
Concepts Taught: Physical Science/Chemistry

Note: I have some graphics that go with this that I can e-mail direct to you - rulers, cylinders - that sort of thing.

The Metric System

Section 1

You are familiar with inches, feet, miles, pounds, quarts, and so on. You know that a car will go a certain number of miles per hour. Gas costs a certain of cents per gallon. All these things are measurements in the English system. (this system is called English because it is primarily used in England and the United States, having had its origins in England.)

But, there is another system of measurement. That system is called the metric system. The metric system is based on the number 10. There are, for example, 10 millimeters per centimeter. There are 1000 (10 times 10 times 10) meters per kilometer. (The prefix kilo- means one thousand times - so a kilometer is one thousand times the length of a meter.) There are one thousand milliliters in a liter. (The prefix milli- means “one thousandth of “ - so one milliliter would be one one-thousandth of a liter.)

In chemistry, physics - in fact, all the sciences, the metric system is used. The basic advantage to the metric system is that it is so easy to go from one unit to another. You just multiply or divide by 10. The English system, on the other hand, has no consistency between units. This will be discussed more, soon.

Questions: Write the answer in a complete sentence.

1. What is the basic difference between the English and the metric system?
2. To go from one unit to another in the metric system, what do you do?
3. What number is the metric system based on?
4. What does kilo- mean?
5. How many milliliters are there in one (1) liter?
6. Milli- means what?
7. Is a millimeter more or less than a meter? How do you know? By how much?
8. Is a kilogram more or less than a meter? How do you know?
9. If 200 milligrams is 200 one-thousandths of a gram, what would 900 milligrams be?
10. Fill in the blanks:
1 foot = _________inches
1 mile= _________feet
1 quart= ________ounces
1 gallon= _______quarts
1 pound= _______ounces
1 ton= __________pounds
11. If there are 454 grams in a pound (which there are), how many grams are there in 2 pounds? In 5 1/2 pounds?

Section 2

Let’s look at some of the basic units of the metric system:

Here are some basic units of the metric system: (Note: the prefix centi- means one-one hundredth of)

1 meter = 1000 millimeters = 100 centimeters

Note that there are 1000 millimeters (abbreviated mm) per one meter. Note also that there are 100 centimeters (abbreviated cm) per one meter. 1000 is 10 times 10 times 10.) So, per meter there are 100 one-hundredths of a meter per meter.

1 kilogram = 1000 grams 1 gram = 1000 milligrams

Note: kilo- means “one thousand times” the base unit (in this case, the gram.) So, in this case there are 1000 grams (abbreviated g, for grams) in a kilogram. And, there are 1000 milligrams (abbreviated mg for milligrams) in a gram.

1 liter = 1000 milliliters

There are 1000 parts of a liter per liter, so 1000 one-thousandths are equal to 1 liter.

1. What do the following stand for?

(a) milli-_____________ (b) centi-____________ (c) g _______________
(d) kilo-_____________ (e) mg______________ (f) cm_______________
(g) mm______________

2. How many mm are there in one meter?
3. How many milliliters are there per liter?
4. How many milligrams are there per gram?

5. How many kilograms are there in 2.2 pounds? (Remember that there are 454 g in one pound.)

6. How many grams are there in one kilogram?
7. If there are 10 mm per cm (which there are) and you have an object which is 50 mm long, how many cm long is it?

8. Suppose that an object is 50 cm long. Is that more or less than a kilometer? (Kilometer is abbreviated km.) Why do you say that? (in other words, explain how you know that it is more or less than a kilometer.)

9. How many grams are in one (1) pound? _________________
10. What is the abbreviation for the following?

(a) kilometer_____ (b) gram_____ (c) milligram_____
(d) centimeter____ (e) millimeter_____ (f) meter________
11. Is 500 mg less than one gram? How much less than one gram is 500 mg (or, if it is more, how much more than one gram is it?)

12. Divide these out:
(a) 50/100 (b) 480/1000 (c) 98/75

13. What does the following equal? 1000/1000

Section 3

The basic units of the metric system (those units from which others come) are:

(1) the gram (g) for massing things
(2) the liter (abbreviated L) for measuring the volume (capacity) of things
(3) the meter, for measuring the length of things

The prefixes milli- and centi-, if added to any of the base units, mean “less than” the whole unit. For instance, a milligram is less than a gram. A centimeter is less than a meter. A milliliter is less than a liter.

The prefix kilo-, since it means one thousand times the base unit (when added to any of the base units) means that you have more than the base unit. For example, a kilogram is a thousand grams, kilometer is a thousand meters, and so on.

Remember:
(1) milli- means one one-thousandth of (the base unit)
(2) centi- means one one-hundredth of (the base unit)
(3) kilo- means one thousand times (the base unit)

(1) What is the basic unit of length in the metric system?
(2) Name the base units of (a) weight and (b) volume in the metric system.
(3) A kilogram is _________ grams. 1 1/2 kilograms is ________ meters. A milliliter (Abbreviated mL) is ________ liter(s).
(4) mL is the abbreviation for ________. g is the abbreviation for ________.

Problems:
Write the problems and solve them. Attach the paper with your work to this unit.

(1) 10 x 10 = ________ (2) 10 x 10 x 10 = ________
(3) 500 mg = _______ g (4) 80 mL = ____________ L
(5) 1.98 km = _______ m (6) 20 m = ____________ km

(7) 20 g = _________ mg (8) 25 cm = ____________ m
(9) 50 m = _________ cm (10) 9.75 kg = __________ g

Activities: Record on your own paper what you find out in each activity.

The materials for these activities will all be found in one place. Ask and you will be told where that is. You should have a meter stick, a 12 inch ruler, a graduated cylinder, a quart jar, and paper and pencil. (You supply the paper and pencil.) Write all responses in complete sentences.

(1) Obtain a meter stick and a 12 inch ruler. Measure (using the ruler) how many inches there are in a meter.
(2) Measure how many inches there are in a cm.
(3) Measure how many cm there are in an inch.
(4) Get the graduated cylinder and measure how many milliliters there are in one quart. You do this by filling the quart jar with water, and pour the water into the cylinder. You will have to fill the cylinder to the top white line, empty it, recording the fact that you had, say, 50 mL and go through the process again, until you empty the jar. The last water you pour into the cylinder probably won’t fill it, so you have to read the amount of water off of the graduated cylinder scale. (Each line with a number beside it is 1 mL; the little lines in between the whole number lines are .1 (one-tenth) of a mL.

(5) Find out how much you and each person in the group weighs. (Estimate if you do not know for sure.) Then remembering that 1 lb. is equal to 454 grams, figure out how many grams and then how many kilograms each of you weigh. Record each person’s name, weight in pounds, weight in grams, and weight in kilograms. Create a chart to record the data.

What you have discovered in steps one through four are some of the basic conversion factors for converting from measurements in the English system to measurements in the metric system. Conversion factors are those equalities which allow for direct conversion from one system to another without having to remeasure everything.

Questions:

(1) What is a conversion factor?
(2) What are conversion factors used for?

One the next page you will find a list of the common conversion factors. You will need to know these to work metric conversion problems.

Activity:

(1) Write a paragraph on the metric system, or
(2) Explain how the metric system is more useful than the English system of measure, or
(3) You and the members create a short skit to illustrate some aspect of the metric system.

Table of Conversion Factors for Metric to English and English to Metric:

1 pound = 454 grams

1 kilogram = 2.2 pounds

1 mile = 5280 feet

1 quart = 32 ounces (fluid ounces, abbreviated fl. oz.)

1 gallon = 4 quarts

1 meter = 1000 millimeters

1 meter = 100 centimeters

1 centimeter = 10 millimeters

1 meter = 39.37 inches

1 inch = 2.54 cm

1 gram = 1000 milligrams

1 kilogram = 1000 grams

1 metric ton = 1000 kilograms

1 ton = 2000 pounds

1 mile = 1.6 kilometers

1 liter = 1.06 quarts

1 quart = 0.946 liters

1 liter = 1000 milliliters

1 pound = 16 ounces

1 foot = 12 inches

1 yard = 3 feet

Abbreviations Used for Various Units:

Ounces - oz. Mile - mi. Meter - m
Liter - L Milliliter - mL Gram - g
Pound - lb. Quart - qt. Foot - ft.
Inches - in. Yard - yd. Kilometer - km
Gallon - gal. Milligram - mg Millimeter - mm
Centimeter - cm Kilogram - kg Ton - no abbreviation
Fluid ounces - fl. oz. Metric ton - no abbreviation 