Lab 1: Metric System

All living things are organized. This organization extends to all the measurable parameters of a living structure (size, weight, surface area, and energy). Scientists use a system of measure called the Metric System to record measurable parameters. The objectives of this laboratory exercise are: to become more familiar with the rational for using the Metric System, become proficient in the collection of biological information using metric measurements, demonstrate an ability to convert between units of metric measurement.

Rational

Why Metric? The metric system utilizes standard units derived from natural systems. Other commonly used systems of measure e.g. english system use units that often have no natural relevence to earth processes or a relationship between measured units. In many cases the units were created based on the physical features associated with a ruling monarch.

Exercise 1: Using the internet links provided below, answer the following questions:

In the United States of America, we currently use the English system to assess everyday measurements of length, weight, and temperature. 1) What are the standard English units for these measurements? 2) Who is responsible for the creation of these units? 3) What rational (if any) is behind the formulation of the unit?

Scientists use the Metric System of measure for everyday data collection. 1) What are the standard metric units for length, mass, temperature, and volume? 2) What is the rational behind each metric unit?

Internet Resources

 National Institute of Standards and Technology
 Background on the SI
 Current definitions of the SI units
 Metric Internet Links
 METRIC STYLE GUIDE FOR THE NEWS MEDIA
 NSTA: Scope, Sequence, and Coordination

 Educational Resources
 
 Pennsylvannia State University  Metric System
 Johnson County Community College  The Metric System (Systeme International)
 Colorado State  Commonly used metric system units, symbols, and prefixes
 Sam Houston State University  Ch.1: Metric System
 L. A. Pierce College  The Metric System

Conversions

Often the standardized unit for each kind of measurement is to large (or small) to measure the intended object. We must use units of measure that are fractions or multiples of the standard units. For example, if we measure a window using the english system it might measure 23 3/4 inches. This measure uses both multiples and fractions of the unit inches. The Metric System also allows for multiples or fractions of a unit to be measured except that instead of using fractions with variable denominators the unit size is variable. Unit size varies based on multiples of 10. The particular unit size to be measured is reflected in the prefix preceeding each unit measurement. The chart below lists commonly used prefixes (in bold) and their reflective relationship to the standardized unit of measure.

 Unit
 Equivalent
 kilometer (km)  1000 meters

 Meter
 1 meter
 decimeter (dm)  1/10 meter
 centimeter (cm)  1/100 meter
 millimeters (mm)  1/1,000 meter
 micrometer (um)  1/1,000,000 meter
 nanometers (nm)  1/1,000,000,000 meter

To directly compare data measurements, it may be necessary to convert all measurements to a common unit value. In the example below, if we wish to compare the height of two animals where the first animal was measured in centimeters and the second animal was measured in millimeters we may wish to compare their height in millimeters.

Animal 1) Height = 90 cm
Animal 2) Height = 45 mm

This would require us to convert the height of animal 1 from a value measured in centimeter units into a value reflecting millimeter units.

To convert from one metric unit value to another requires two steps. Step 1: Ask yourself, is the value I am converting to larger or smaller than the original unit size. Using the example above: the measure of animal 1 height must be converted from centimeter to millimeter units because we wish to compare height measurements in millimeter units. Answer: millimeter units are smaller than centimeter units (1mm=1/1000 m whereas 1cm=1/100 m).

If the unit value you are converting to is smaller than the original unit value then a multiplication function will be used.
If the unit value you are converting to is larger than the original unit value then a division function will be used.

Let's use an example that is familiar to us: How many pennies are there in a dollar bill? To convert our value from dollar to pennies we must multiply (the number of pennies will exceed the number of dollars even though the total value of the transaction remains the same).

Likewise, It is important to remember that when we are converting units from one unit size to another unit size that the total value of the measurement remains the same only the size of each unit has changed.

Step 2 requires us to know the difference in size between the units to be converted. This "difference" between unit size will be the value that we will either multiply or divide for the conversion. In the example above we are converting centimeter unit into millimeter units. From the earlier chart we know that:

1 centimeter= 1/100m
1 millimeter = 1/1000m therefor 1 cm is 10 times greater in value than a millimeter. "Difference" is 10.

If both values are expressed as fractions of the same reference (in this case "m") then cancelling out the zeros can help expose the "difference between the unit values. By cancelling zeros (multiplying each value by a common number) above we get:

1 centimeter = 1/100m x 100= 1/1 0r 1
1 millimeter = 1/1000m x 100=1/10 so a centimeter is 10 times larger than a millimeter

So to solve our original problem: What is the height of animal 1 in millimeters? we do the following:

Step 1: the unit value we are converting to is smaller than the original unit value so we will multiply (x).
Step 2: the "difference" between unit values is 10.
Answer: 90cm = __ mm is answered by 90x10 =900mm

The conversion format followed above works for any metric conversion you will be asked to do reguardless of the unit of measure being collected. It is important that you be able to recognize and undrstand the meaning behind the prefixes outlined earlier.

Measurements

Most metric measurements are obtained using devices that you have been using to collect English measurements.

Length
Metric length is collected with a ruler measured in meter (m), centimeter (cm), and/or millimeter (mm) units. We use this instrument the same way we would use a foot ruler or yard stick of the english system. Obtain a meter stick and centimeter ruler from the supply table.

Locate the centimeter and millimeter markings.

How many centimeters are there in the meterstick?
How many millimeters are there in the meterstick? (Hint: count how many millimeters in 1 centimeter)
How long is the centimeter ruler in cm? In mm?

Practice using the centimeter ruler or meter stick to measure objects around the room (table, chair, classmates, shoe, pencil) until you are comfortable recording length in metric units.

Practice converting your measurements from one unit value of length to another. Try these. Use your centimeter ruler to assist if necessary.

10 cm = ___mm
25 mm = ___cm
95 cm = ___m
0.75m = ___cm = ___mm
5.5mm = ___m (tough one)
11.5cm = ___mm = ___m

Mass
Mass is measured in gram (g) units and is a measure of how much substance an object consists of. Mass differs from weight because it is unaffected by gravity. The mass of an astronaut on Earth or the moon is constant even though the weight of the astronaut is less at the moon than on Earth. To measure mass we use a balance. Mass is calculated with a balance similar to how an object might be weighed.

Place an object in the pan of the balance. The arm of the balance is no longer centered but rests above the center indication line. Using the counterbalances of known mass (1g, 10g, or 100g), slide the counterbalances toward the right until the arm rests at the centerline. If the arm falls below the centerline, move the counterbalance towards the left. Practice balancing other objects from around the room.

Practice converting your measurements from one unit value of mass to another. Try these practice problems.

150 mg=___g
1500g=___kg
950ug=___mg
2500ug=___g
1.5kg=___mg

Volume
Volume is a measured in liter (l) units and is a measure of how much space an object occupies. Volume is a cubic measurement meaning that in order to calculate volume a scientist needs to consider not only the length and width of an object but also the height. Liquids and gases conform to the shape of the container they occupy. (Coffee poured out of a pot conforms to the shape of the cup). To calculate the volume of a liquid a scientist needs only to pour the solution that is being measured into a container of known volume. Scientists usually use a container called a graduated cylinder to measure the volume of a liquid.

Graduated cylinder module

When measuring the volume of a liquid it is important to remember that liquids often adhere to surfaces. Place some liquid in a graduated cylinder and look at the meniscis (where the liquid meets the air). Notice that the meniscis is bent such that the edges are higher than the center. To get an accurate measure of volume, read the middle (lowest point) of the meniscis. It is also important to have your eyes at the same level as the meniscis when reading the measurement.

Calculating volume for solid objects can be more difficult. Remember that volume is a cubic measurement. There is a relationship between length measurements and volume (liter) measurements. 1cmx1cmx1cm= 1ml so 1cm(cubed) or cc =1ml. The volume of objects conforming to standard geometric shapes can be calculated relatively easily using geometric formulas for volume. Measurement must be converted to centimeters prior to multiplying:

 shape geometric formula
 square  LxWxH
 rectangle  LxWxH
 cylinder  (2pi*r)xH
 triangle  1/2(LxWxH)

Unfortunately, most objects are a mixture of geometric shapes or do not resemble standard shapes at all. An easier way of measuring volume for most solids is to emmerse them in fluid and calculate displacement (the amount of fluid they push out of the way). If you measure the fluid level in a graduated cylinder then add a solid object to the same cylinder, you will notice that the fluid now measures at an increased volume (the fluid level is higher). The displaced volume ( the final volume - the initial volume) is the volume measurement of the solid. We can observe this phenomenon when taking a bath. If a person fills the tube to the brim then jumps in what happens to the water? Practice measuring volume of other objects from around the room.

Practice converting your measurements from one unit value of volume to another. Try these practice problems.

650 ml=___l
87ml=___ul
8550ul=___l
2500nl=___ul
1.5ml=___ul

Temperature


Temperature is measured in degrees celsius (or centigrade). Most metric temperatures are measured with a thermometer calibrated in celsius units but occassionally you may have to convert english units (degree Fahrenheight) to degrees celsius. A metric unit of degree is larger than an english degree unit so we must use a formula to convert the two measurements. The formula is:

degrees celsius= 5/9 (degrees fahrenheight - 32)

The formula depicts two differences between the two degree scales. 1) Recall that the celsius scale has a zero at the point where water freezes. At what temperature does water freeze using the farenheight scale? To equalize our zero points we must first subtract 32 from our farenheight value. 2) 5/9 reflects the size difference between the degree units of the two scales. This is best represented by comparing the two scales at two different places. Using the diagram below we see that water freezes at zero celsius and boils at 100 celsius, a range of 100 degres. Corresponding values of degrees Farenheight are 32 and 212, a range of 180 degrees. So we see that 100 degrees change in celsius units reflects 180 degrees change in Farenheight units. To compare these units directly we can write the differences as 100/180. Dividing by a commonvalue of 20, our fraction is reduced to 5/9. The equation value 5/9 therefor reflects the difference in degree size between degrees celsius and Farenheight. For every 5 degrees change in celsius there are 9 degrees change in Farenheight.

Practice measuring the temperature of other objects or liquids from around the room.