The Metric System and Measurement

Transcription

1 Introduction The Metric System and Measurement The metric system is the world standard for measurement. Not only is it used by scientists throughout the world, but most nations have adopted it as their standard of measurement. All of the measurements done in this course will use the metric system. The table below shows the standard unit of length, weight, volume, and temperature in the metric system. It also shows the English equivalent. Metric English Length meter inches Weight gram ounces Volume liter quarts Temperature degree (Centigrade) 1.8 degrees Fahrenheit Meters, grams, and liters (see the table above) form the basis for larger or smaller units. The units are named using these prefixes: Kilo = 1000 Deci = 1/10 Centi = 1/100 Milli = 1/1,000 Micro = 1/1,000,000 Nano = 1/1,000,000,000 The table below shows how meters are related to five other measures of length. Unit Length kilometer (km) 1,000 m (1 X 10 3 m) meter (m) 1 m centimeter (cm) 0.01 m (1 X 10-2 m) millimeter (mm) m (1 X 10-3 m) micrometer (um) m (1 X 10-6 m) nanometer (nm) m (1 X 10-9 m) Notice that each of the units in the table above are related to meters by a multiple of 10. The photograph below shows the end of a meter stick. The 90 cm mark can be seen in the center of the photograph. One meter = 100 cm. Notice that each centimeter is divided into 10 mm. 1 of 10 9/20/16, 3:45 PM

2 The tables below show similar units based on grams (weight) and liters (volume). Unit Weight metric ton (t) 1,000 kg or 1,000,000 g (1 X 10 6 g) Kilogram (kg) 1,000 g (1 X 10 3 g) gram (g) 1 gram milligram (mg) g (1 X 10-3 g) microgram (ug) g (1 X 10-6 g) nanogram (ng) g (1 X 10-9 g) Unit Volume kiloliter (kl) 1,000 l (1 X 10 3 l) liter (l) 1 l milliliter (ml) l (1 X 10-3 l), 1cm 3 microliter (ul) l (1 X 10-6 l) Notice in the table above that one milliliter (ml) equals one cubic centimeter (1 ml = 1 cc or cm 3 ). Metric Conversions Exponents The table below shows two different ways to write numbers. For example, a second way to write the number 1,000 is 1 X = = 1 X = 1 X ,000 = 1 X = 1 X = 1 X of 10 9/20/16, 3:45 PM

3 Examples 256 = 2.56 X = X = 5.5 X 10-2 Decimal Point Metric conversions are done by moving the decimal point. When converting a large unit such as meters to a smaller unit such as millimeters, the decimal point is moved to the right. When converting smaller units to larger units, the decimal point is moved to the left. You must subtract the exponents in order to determine how many places to move the decimal point. Examples Convert 2.6 cm to um. This problem is solved by subtracting the exponents. The exponent for cm is -2; the exponent for um is -6. Subtract the two numbers: (-2 - (-6) = 4). Therefore, to convert 2.6 cm to um, you must move the decimal point 4 places to the right. 2.6 cm = Convert 57 um to cm. The exponent for um is -6. The exponent for cm is -2. You must subtract these two number to determine how many places to move the decimal point (-2) = -4. The negative sign indicates that you must move the decimal point 4 places to the left. 57 cm = Laboratory Exercise Copy and paste problems from each section below into a Word document to be turned in at the end of the semester in a notebook with the rest of the online lab assignments. You will be given one grade (out of 100 pts) for your lab notebook. Be sure to include your name, course: BIOL150 D1, 3 of 10 9/20/16, 3:45 PM

4 Length Weight Name of Assignment, and Date at the top of each assignment. Do not use scientific notation (exponents) or fractions in your answers to the questions below. Write all of the zeros. Measurement of Length Measure the width of this page using a small plastic ruler. Record your measurement in 1) millimeters, 2) centimeters, and 3) meters. Record your answers on the answer sheet. Use a meter stick to measure the width of the laboratory table in 4) millimeters, 5) centimeters, and 6) meters. 7) Which unit of measurement (kilometer, meter, centimeter, millimeter, micrometer, or nanometer) would be most appropriate for measuring the width of this room? Conversions of Length Perform the following conversions. 8) 1 m = cm. 9) 1 cm = m. 10) 3.57 mm = um. 11) 452 cm = mm. 12) 0.04 um = mm 13) 37.6 nm = mm 14) 52 nm = um 15) 0.05 um = nm. 16) 4.3 m = um 17) 4206 mm = cm 18) mm = nm 19) 4.8 cm = um Use the following information to perform the calculations below. Metric to English: 1 meter = inches = feet English to Metric: 1 inch = meters; 1 foot = meters 20) 8.53 inches = m Round your answer to the nearest m. 21) 12 feet, 3 inches = m Round your answer to the nearest 0.01 m. Measurement of Weight The laboratory scale shown below has a sensitivity of g. Due to its sensitivity, moving air will cause it to fluctuate. The glass chamber surrounding the weighing pan prevents air currents 4 of 10 9/20/16, 3:45 PM

5 from interfering with the weight. The scale in the photograph below has a sensitivity of 0.01 g. The scale can be set to zero by pressing the zero (tare) button on the lower left part of the scale. Place a small beaker on the pan of the scale and zero it by pressing down on the zero (tare) button located on the front of the scale. Place a penny in the beaker to obtain its weight. 5 of 10 9/20/16, 3:45 PM

6 22) How much does the penny weigh in grams? Remove the beaker from the scale and weigh the penny without using the beaker. You must first zero the scale before weighing the penny. Conversions of Weight Perform the following conversions. 23) 37 g = mg 24) mg = g 25) g = kg Use the following information to perform the calculations below. Metric to English: 1 g = ounces = pounds English to Metric: 1 ounce = grams; 1 pound = grams 26) 150 pounds = kg Round your answer to the nearest 0.01 kg. 27) 3 oz = g Round your answer to the nearest 0.01 g. Volume Measurement of Volume Obtain a 10 ml graduated cylinder (shown below) and fill it about half full with water. 28) Hold the graduated cylinder in a vertical position at eye level and read the number of milliliters of water that are in the cylinder. Be sure to read the water at the bottom of the meniscus. The arrow points to the bottom of the meniscus in the photograph below. What is the volume of water in the cylinder? 6 of 10 9/20/16, 3:45 PM

7 Use a 50 or 100 ml graduated cylinder to determine the amount of liquid that a test tube can hold (it's volume). 29) How did you determine the volume of the test tube? Conversions of Volume 30) 42 ml = l 7 of 10 9/20/16, 3:45 PM

8 31) 27 ul = l 32) 3.6 l = ml 33) 1 ml = ul Sometimes volume is measured using cubic centimeters (abbreviated cc or cm 3 ). One cubic centimeter equals one milliliter (1cc = 1ml). 34) 27 l = cc (or cm 3 ) Use the following information to perform the calculations below. Metric to English: 1 liter = quarts = gallons English to Metric: 1 quart = liters; 1 gallon = liters 35) 2.3 quarts = liters Round your answer to the nearest 0.01 liter. 36) 0.5 gallons = liters Round your answer to the nearest 0.01 liter. Temperature Measurement of Temperature The following temperature measurements should be done in Centigrade (Celsius): 37) Calculate the temperature of the air in the laboratory room if the thermometer reads 98 F. 38) Calculate the temperature of ice water if the thermometer reads 34 F. 39) Calculate the temperature of boiling water if the thermometer reads 212 F. Conversions of Temperature The temperature in Fahrenheit can be converted to Centigrade (Celsius) using the formula: C = 5/9( F - 32) For example, to convert 60 F to C, subtract 32 (=28), multiply it by 5 (=140) and divide it by 9 (=15.56). The steps listed above are performed in reverse order to convert Centigrade to Fahrenheit. The equation is below: F = (9/5 C) + 32 For example, 20 C is converted to F by multiplying it by 9 (= 180), dividing it by 5 (= 36), and adding 32 (=68). 40) 72 F = C For this one, use the formula C = 5/9( F - 32). Round your answer to the nearest 0.1. (Note- If you do not have a calculator, use the one on the computer. Click Start, Programs, Accessories, Calculator). 8 of 10 9/20/16, 3:45 PM

9 41) 37 C = F For this one, use the formula F = ( 9/5 C) + 32 What is DENSITY? Density = Mass/Volume Density is an intensive property of matter that is defined as the ratio of an object's mass to its volume. Mass is the amount of matter contained in an object and is commonly measured in units of grams (g). Volume is the amount of space taken up by a quantity of matter and is commonly expressed in cubic centimeters (cm 3 ) or in milliliters (ml) (1cm 3 = 1 ml). Therefore, common units used to express density are grams per milliliters (g/ml) and grams per cubic centimeter (g/cm 3 ). Let's look at an example. A typical brick has a mass of 2,268 g and occupies a volume of 1,230 cm 3. The density of the brick is therefore: 2,268 g/1,230 cm 3 = 1.84 g/cm 3 Density is an easy concept to confuse. For example, many items that we commonly think of as "light" or "heavy" do not have different masses, but they do have different densities. Look at the table below for examples of the densities of common substances. Density of Some Common Substances Substance Density (g/cm 3 ) Air Feathers Wood(Oak) Ice 0.92 Water 1.00 Bricks 1.84 Aluminum 2.70 Steel 7.80 Silver Gold of 10 9/20/16, 3:45 PM

10 Density Problems 42) What is the volume of a tank that can hold Kg of methanol whose density is 0.788g/cm 3? 43) What is the density of a board whose dimensions are 5.54 cm x 10.6 cm X 199 cm and whose mass is 28.6 Kg? 45) CaCl 2 is used as a de-icer on roads in the winter. It has a density of 2.50 g/cm 3. What is the mass of 15.0 L this substance? 46) Measure the length of a pencil in inches and cm. 47) Measure the length of a TV remote control in inches and cm. 48) Measure the length of a credit card or business card in inches and cm. 49. Measure the diameter of a CD-Rom in inches and cm. 50. Measure the length of the width of a sheet of paper in inches and cm. References and Credits System/Metric_System.htm of 10 9/20/16, 3:45 PM