1. Measure Objects Using the Metric System

Metric System

Behavioral Objectives:

You should be able to 1. Measure objects using the metric system. 2. Make conversions within the metric system. 3. Have a basic understanding of the metric system as compared to the English system.

Metric System: We have been trained to measure lengths in such units as inches, feet, yards and miles and volume of things in pints, quarts and gallons. Temperatures are measured in degrees Fahrenheit.

The English system of measurement which we are familiar with, grew out of the creative way that people measured items for themselves. Familiar objects and parts of the body were used as measuring devices. For example, people measured shorter distances on the ground with their feet. They measured longer distances by their paces (a "mile" was a thousand paces). They measured capacities with common household items such as cups, pails, and baskets. The word gallon comes from an old name for a pail.

Unlike us, most countries in the world use degrees Celsius instead of Fahrenheit for temperature and an alternate system, called the metric system, for measurement of distance, volume, etc.. Indeed, the rest of the world and the scientific community long ago recognized that the metric system was much more efficient and so much easier to use!

Children are now being taught both systems of measurement. If you go to Sears to buy a measuring tape you find that they sometimes put a metric scale on the side opposite to the one with inches. Take a look at your car’s speedometer and you will note the speed is indicated in both miles and kilometers per hour. Since all major countries, except the United States, have already accepted the metric system, we have to convert our measurements if we wish to sell our products in the world market.

The metric system, once you once master it, is so much easier and convenient to use that you will wonder why we have not changed to this system. Any “metrification” of the United States would be a costly and slow process. For instance, many of the tools and wrenches which you now own are calibrated in inches. Most of the machines used in industry are currently tooled in inches. A changeover to the metric system was planned years ago but was never completed. The major advantage of the metric system is that the units are based on multiples of ten; this is called a decimal system. Thus, converting from one set of metric units to another simply involves moving the decimal point in one direction or another. Unfortunately, this cannot be done easily in the English system. To illustrate: try figuring out how many inches there are in 3 ½ miles. It gets really complicated. But an equivalent conversion can be made in similar metric units just by sliding the decimal point over. There are no fancy conversion factors which need to be used!

The basic metric units of measurement are the meter (for length), the liter (for volume) and the gram (for weight or mass). These are the “fundamental units” used below. To conveniently specify various sizes of measurements, prefixes are added before the word meter, liter and gram.

Micro = 1/1,000,000 of the fundamental unit Milli = 1/1000 of the fundamental unit Centi = 1/100 of the fundamental unit Deci = 1/10 of the fundamental unit Deka = 10 times the fundamental unit Hecto = 100 times the fundamental unit Kilo = 1000 times the fundamental unit

The fundamental unit is either the meter, the liter, or the gram.

Examples of the use of these prefixes:

• A millimeter is 1/1000 of a meter in length. Since the meter is slightly longer than a yard, a millimeter is a little bit longer than the diameter of the period at the end of this sentence.

• A centimeter would be about 1/100th of a meter in length. (2.54 centimeters = 1 inch).

• Likewise, a decameter would be 10 meters long and a kilometer is 1000 meters long.

• Several years ago, there was a coin in the United States currency which was called a ‘Mill’. The value of these coins was 1/1000th of a dollar – the same as 1/10th of a penny. Because of inflation we no longer use the mill as a coin. However, in voting for bond issues sometime the denomination is used to indicate the amount of tax money being appropriated. In this class, you will commonly use the prefixes micro-, milli, centi, and kilo along with the fundamental unit.

You will sometimes use the term micron [µ] or micrometer for distance. This is 1/1,000,000 of a meter and is a very small distance. 1000 microns = 1 millimeter. 1,000,000 microns = 1 meter

Metric unit of length

The metric unit of length is the meter. The prefixes are applied to the word meter as follows:

1 micron (or micrometer) [µ] = 1/1,000,000 meter 1000 microns [ µ] = 1 millimeter (mm) = 1/1000 meter 10 millimeters = 1 centimeter (cm) = 1/100 meter 10 centimeters = 1 decimeter (dm) = 1/10 meter 10 decimeters = 1 meter (m) 10 meters = 1 dekameter (dk) = 10 meters 10 dekameters = 1 hectometer (hm) = 100 meters 10 hectometers = 1 kilometer (km) = 1000 meters

We can use the micron (micrometer) to measure objects under the microscope; we will mostly use millimeters and centimeters for longer measurements of length. The following are examples of conversion within the metric system.

Let’s convert from millimeters to centimeters. You will be asked to convert between various metric lengths in the lab. The process is basically a multiplication or a division utilizing units of 10s (decimals). A divisional decimal movement is to the left: a multiplication decimal movement is to the right.

For example, a line has been measured at 27 millimeters in length. 10 millimeters = 1 centimeter. 27/10 = 2.7 centimeters (cm) (move decimal point to the left for each unit of 10). To convert centimeters to millimeters, multiply by 10.

For example, suppose a line measured 5.2 centimeters in length. 5.2 x 10 = 52 millimeters (mm) (move decimal point to the right for each unit of 10) There are 1000 microns in a millimeter. To convert millimeters to microns, multiply by 1000.

For example, suppose a line measured 1.8 millimeters in length. 1.8 x 1000 = 1800 microns (move the decimal point to the right for each unit of 10, or 3 places over)

To convert microns to millimeters, divide by 1000.

For example, suppose a line measured 1100 microns in length.

1100/1000 = 1.1 millimeters (move the decimal point to the left for each unit of 10 or 3 places)

For your information:

The following are equivalent to the metric and English System for length.

1 centimeter = 0.39 inches 1 meter = 39.37 inches 1 kilometer = 0.62 miles 1 inch = 2.54 centimeters

In this class, you will not need to covert from the English system to the metric system and vice versa. (Phew!)

Sample Problems: Work the problems in the space below, show your work and record your answers in the space provided. The answers will be found on the next to last page of this packet.

1. Convert 22 millimeters to centimeters: answer: ______

2. Convert 9.7 centimeters to millimeters: answer: ______

3. Convert 2.2 millimeters to microns: answer: ______

4. Convert 5500 microns to millimeters: answer: ______

5. Convert 1.5 centimeters to microns: answer: ______Measurement of Volume

The metric unit of volume is the liter. In this class we will commonly use only milliliters and liters. NOTE: The milliliter is equal to one cubic centimeter (cc).

There are 1000 milliliters in a liter. To convert milliliters to liters, divide by 1000.

For example, convert 550 milliliters to liters. 550/1000 = 0.550 liters (move the decimal 3 places to the left)

To convert liters to milliliters, multiply by 1000.

For example, convert 2.5 liters to milliliters. 2.5 x 1000 = 2500 milliliters (move decimal 3 places to right)

The following are equivalent in metric and English system (conversion factors for volume)

1 milliliter = 0.034 fluid ounces 1 liter = 1.06 quarts 1 milliliter = 1 cubic centimeter (cc)

In this class, you will not need to covert from the English system to the metric system and vice versa. (Phew!)

Problems: work the following problems in the space below. Show your work and record your answers in the space provided. The answers will be found on the next to last page of this packet.

1. Convert 225 milliliters to liters: answer: ______

2. Convert 1.8 liters to milliliters: answer: ______

Measurement of Weight

The metric unit of weight/mass is the gram. The commonly used prefixes are applied to the unit gram as follows:

Gram (g)

Milligram (mg) = 1/100 gram Kilogram (kg) = 1000 grams

There are 1000 milligrams in a gram. To convert milligrams to grams, divide by 1000.

For example: convert 1250 milligrams to grams. 1250/1000 = 1.250 grams (move decimal 3 places to the left)

To convert grams to milligrams, multiply by 1000.

For example: convert 1.755 grams to milligrams. 1.755 x 1000 – 1755 milligrams (move decimal 3 places to the right)

There are 1000 grams in a kilogram. To convert grams to kilograms, divide by 1000.

For example: convert 900 grams to kilograms. 900/1000 = 0.9 kilograms (move decimal 3 places to the left)

To convert kilograms to grams, multiply by 1000.

For example: convert 2.435 kilograms to grams. 2.435 x 1000 = 2435 grams (move decimal 3 places to the right)

The following are equivalent in the metric and English systems. (conversion factors for weight)

1 gram = 0.0345 ounces 1 kilogram = 2.2 pounds 454 grams = 1 pound 28.24 grams = 1 ounce

Again, don’t worry about these conversions!

Problems: Work the following problems in the space below. Show your work and record your answers in the space provided. The answers are found on the next to last page of this packet.

1. Convert 1127 milligrams to grams: answer: ______2. Convert 0.285 grams to milligrams: answer: ______

3. Convert 1333 grams to kilograms: answer: ______

4. Convert 2.455 kilograms to grams: answer: ______

Temperature (conversion for temperature)

Most scientific measurements of temperature are made using the Celsius or Centigrade scales. This is abbreviated as C. The Fahrenheit scale which you commonly use compares with the Celsius scale as follows:

Fahrenheit Celsius Freezing point of water 32 0 Room temperature (average) 72 22 “Mean” human oral temperature 98.6 37 Boiling point of water 212 100

The Celsius scale uses the freezing point of water as its zero mark and the boiling point of water as the 100 degree mark, and there are 100 equal units of degrees between these two extremes. If you learn the four conversions above, you will have little trouble working with the Celsius scale in this class.

The Fahrenheit degrees may be converted to Celsius degrees with the following formula*.

C = 5/9 (F-32)

Celsius degrees may be converted to Fahrenheit degrees with the following formula*.

F = 9/5 C+32

* Don’t worry, you will not be required to know or use these formulas!

Here’s another way to figure out the conversions.

To go from a small to greater measurement, divide by a multiple of ten!

Divide ------

/10 /10 /10 /10 /10 /10 /10 /10 /10 micro- milli- centi- deci- unit of deka- hector- kilo- ( µ) (m) (c) (d) measure (dk) (h) (k) g, m, l x 10 x10 x10 x10 x10 x10 x10 x10 x10 ------Multiply

To go from a greater to a smaller measurement, multiply by a multiple of ten!

Abbreviations Here are some common abbreviations for metric system values:

Abbreviation Meaning cm centimeter mm millimeter m meter km kilometer L liter mL milliliter µL microliter dL deciliter µg microgram kg kilogram mg milligram

You will be using some of these in class. Metric System Answers

Length

1. 2.2 centimeters 2. 97 millimeters 3. 2200 microns 4. 5.5 millimeters 5. 1.5 cm = 15 mm = 15.000 microns

Volume

1. 0.225 liters 2. 1800 milliliters

Weight

1. 1.127 grams 2. 285 milligrams 3. 1.333 kilograms 4. 2455 grams Name: ______Metric System Practice Problems (to be turned in with Laboratory Exercise 1)

1. 88 millimeters = ______centimeters

2. 9876 milliliters = ______liters

3. 3.5 liters = ______milliliters

4. 2200 milligrams = ______grams

5. 650 grams = ______kilograms

6. 7.6 kilograms = ______grams

7. 0.125 grams = ______milligrams

8. 365 meters = ______kilometers

9. 2500 micrograms = ______milligrams

10. 89700 milliliters = ______liters

11. 94.3 kg = ______mg

12. 98 g = ______kg

13. 9 m = ______mm

14. 7656 ml = ______L

15. 6600 mm = ______m