The Metric System & Conversions

Transcription

1 Purpose of this lab: The purpose of this lab exercise is for you to become familiar with basic measurements in metric units (SI), English units, and conversions between the two systems. Assignment Objectives: 1.) Learn common metric units of length, mass, volume and temperature; 2.) Convert between the metric and English systems. SI Metric System (International System of Units) Scientists in most countries use the International System of Units (SI metric system) to communicate their findings to the international scientific community. This system was developed in France in the late 1800 s to coordinate and unify reporting of scientific information. The metric system is used throughout the world today in the scientific community, however the United States continues to use the Imperial System (English) when conveying non-scientific measurements (miles, feet, inches). Metric is the system of choice by most scientists because it is based on a logical system of multiples or fractions of 10. In both English and Metric systems, base units are the fundamental units for expressing a desired physical quantity. For instance, in the Metric system, base units for quantities of distance, fluid volume, and mass are the meter, liter, and gram, respectively. Equivalent base units in the English system are the foot, quart, and ounce, respectively (Table 1). Table 1. Common Metric and English base units, their symbols, and the quantities they express. M e t r I c SI Unit SI Base Units of Measure Symbol meter distance m liter volume or capacity l kilogram mass* kg E n g l I s h English Unit Base Units of Measure Symbol foot distance ft quart volume or capacity qt ounce weight* oz * Mass is a measure of the amount of matter an object has, whereas weight is a measure of how much of the force of gravity is exerted on an object. Because mass and weight on Earth are directly related to gravity, the terms are often used interchangeably. The metric system is based on multiples or fractions of the number 10, making an easier measurement system than the U.S.-Imperial System. Table 2 lists the prefixes used in the metric system and what they mean. The prefixes, mega, kilo, hecto, and deca (from Greek) 1

2 express the meter as a multiple of 10. The prefixes: deci, centi, and milli (from Latin) express the meter as a fraction of 10. Table 2. Prefixes used in the metric system and their meanings. A prefix precedes a base unit to designate how many times more than or what fraction of the base unit is expressed. Metric Prefixes 1 gigamegakilohectodecadecicentimillimicronanno- Their Meaning a billion base units a million base units a thousand base units a hundred base units ten base units 1/10 of a base unit 1/100 of a base unit 1/1000 of a base unit 1/1,000,000 of a base unit 1/1,000,000,000 of a base unit A given base unit (i.e. meter) can be expressed as either multiples of that base unit or a fraction of that base unit by powers of 10. A kilometer equals 1000 meters and is obtained by multiplying 1 meter by The prefix kilo prompts the user to multiply the base unit meter by In a similar manner, fractions of a meter can be obtained by multiplying a meter either by 0.1 to obtain 10ths of a meter or decimeters, by 0.01 to obtain 100ths of a meter or centimeters, or by to obtain 1000ths of a meter or millimeters. Base Units of Measure a little discussion Length Let s do some mental conversions of SI units from the imperial measurements. Below are some hints to help you relate the two systems. A meter equals about 3 feet or a yard (3.28 feet) 1 km equals about half a mile (.62 miles) The thickness of a paper clip measures about 1 mm The diameter of a DVD or CD is about 12 cm or 120 mm The following should help you remember which units of length are smallest and largest. Units of length millimeter (mm) smallest value centimeter (cm) decimeter (dm) meter (m) kilometer (km) largest value 2

3 Volume Volume describes the amount of space within a three-dimensional object. Figure 1 shows a cube that measures 1 cm in each dimension (width, height, and depth). To calculate the volume of the cube, multiple the three dimensions (length x width x height). So the volume of the cube = 1 cm x 1 cm 1 cm, or 1 cm 3 which is also equal to 1 milliliter (1ml). Figure 1. Drop of water fills the cube = 1 ml 1cm 1cm 1cm The following hints should help you relate to the metric units of volume. A sugar cube = 1 ml A liter (l) of soda = 1000 ml About 4 liters = 1 gallon Mass Mass is the amount of material contained within an object, or put another way, matter is anything with mass. The more matter, the more mass. The mass of an object is a fixed quantity. The English base unit weight is not mass; it is mass being acted on by gravity. The weight of an object will vary at different locations on Earth s surface since gravitational forces vary from place-to-place. The following might help you relate to the metric units of mass: Units of mass milligram (mg) smallest value gram (gm) kilogram (kg) largest value Some common objects and their mass: A paper clip weighs about 1 gm A penny weights 2.5 grams A nickel weights 5 grams 1 liter of water (or soda) = 1 kg 1 cubic meter of water (1 m 3 ) = 1000 liters 1000 liters = 1000 kg or 1 metric ton (the weight of a small car) 3

4 PROBLEMS in MEASUREMENTS and CONVERSIONS A Useful Arithmetic Method: Proportions or Dimensional Analysis Converting between either the different metric units or between metric and English units can be done easily with the method of proportions or Dimensional Analysis. Example A: Knowing that 1 meter = 100 cm, how many cm are in 3 meters? Step 1: Set-up the proportions by keeping the same units, meters in this example, in the numerator, and the same units, centimeters (cm) in this example, in the denominator as follows: 1meter 100cm = 3meters X Step 2: Cross-multiply and solve for X, which then equals 300 cm. Example B: Express 11 cm in meters. Step 1: Knowing that 1 cm = 1/100 m or 0.01 m, set up the proportions as follows, keeping cm in the numerator and m in the denominator. 1cm 0.01m = 11cm X Step 2: Cross-multiply and solve for X, which then equals 0.11 m Converting From One Metric Unit to Another It is important to understand if the metric unit in question is a fraction or a multiple of the base unit (liter, gram, or meter) in a given problem. Use Table 2 to help solve problems 1a, 1b, and 1c below. 1a. What part or fraction of a meter is the centimeter? b. Determine how many cm are in 2.75 meters. c. Express 66 cm in terms of a meter: 4

5 Measuring Length 2. Lab partners are needed for this problem. Use a 2- meter stick and measure each others height to the nearest cm. height: cm convert to meters: m 3. Use a 1- meter stick or tape to measure the longest surface dimension or diameter of your lab table- top. Record measurement in meters, then convert to centimeters: longest table- top dimension: convert to centimeters: cm m Measuring Volume 4. Measure 3 ½ inches up from the bottom of a disposable cup, and mark this level on the inside of the cup with a permanent marker. Fill to this level with water. Pour the water into a graduated cylinder to measure the fluid volume, in milliliters (ml). ml Measuring Mass 5. Use a scale for weighing to find the mass in grams for the following Earth materials: a. sample of granite: g c. sample of mantle rock (peridotite): g b. sample of basalt: g d. sample of mantle rock (eclogite): g Converting Between Metric Units 6. Use the method of proportions or dimensional analysis to convert the following units. Attach a separate piece of paper to this lab assignment that shows your calculations. Convert To 3.65 meters (m) centimeters (cm) 17 centimeters (cm) millimeters (mm) 36 centimeters (cm) meters (m) 1 gram (g) milligram (mg) 1 liter (l) milliliters (ml) 489 milliliters (ml) liter (l) 5

6 235 kilometers (km) centimeters (cm) Metric-English Temperature Units Temperature units on any thermometer are always expressed in degrees (symbol o ). Unlike the units of length, volume, and mass in both Metric and English measuring systems, degrees are not expressed as multiples or fractions by moving the decimal. In order to understand how both scales operate and how both can be used interchangeably, first consider how the temperature scales were established. The maximum and minimum end-points for both scales are based on the boiling and freezing temperatures of water, respectively. Centigrade was the former name for the metric temperature scale; referring to its 100 subdivisions. In 1948, by international agreement, the name, Celsius, was adopted for the metric scale after its originator, Anders Celsius, in the early 1700 s. The English temperature scale is named after Fahrenheit (alive from the late 1600 s to the early 1700 s). To convert from Celsius to Fahrenheit and back one must use the following conversion formulas: Celsius to Fahrenheit: o F = (1.8)( o C) + 32 o o C = Fahrenheit to Celsius: 7. If you do not already know them, find in any reference the freezing and boiling temperatures of H 2 O in degrees Celsius, and enter them below. Freezing temperature: Boiling temperature: 8. Take the Celsius values) for the freezing and boiling temperatures of H 2 O (from problem #7and convert them to Fahrenheit values by using the conversion formulas above. Freezing temperature: Boiling temperature: 9. Use a thermometer to read the air temperature of the classroom in degrees Celsius. Enter the value below and, using one of the mathematical formulas above, convert it to degrees Celsius. Classroom temperature in degrees Celsius: to degrees Fahrenheit: 6

7 Converting Between Metric and English Units 10. Use the method of proportions or dimensional analysis and the information supplied in Table 3 to convert the following units: a. 1 inch = cm b. 1 meter = feet c. 1 mile = km d. 1 km = miles e. 1 gallon = liters f. 1 oz = grams g. 1 lb = kilograms 11. The term knot, defined as one nautical mile per hour, is used to measure speed in the ocean (e.g. current speed). A nautical mile is slightly more than a standard mile (also called statute mile). Use the conversions below to answer the following questions. 1 nautical mile = 1.15 miles = 1.85 kilometers 1 knot = 1.15 miles per hour = 1.85 kilometers per hour a. The distance from Long Beach to Avalon on Catalina Island is about 30 statue miles. What is the distance in: nautical miles: kilometers: b. You are in a boat travelling 25 miles per hour. What is the speed in knots: kilometers: 7

8 Table 3. Metric-English conversion factors DISTANCE from Metric to English from English to Metric Metric Unit English Unit 25.4 mm 1 centimeter 0.39 inches 1 inch 2.54 cm 1 meter 1 kilometer 39.4 inches 3.28 feet 1.09 yards 3280 feet 0.62 miles 1 foot 1 mile 30.5 cm m 1609 meters 1.6 km MASS from Metric to English from English to Metric Metric Unit English Unit 1 gram 0.04 ounces 1 ounce grams 1 kilogram 2.2 pounds 1 pound 454 grams 0.45 kilogram VOLUME from Metric to English from English to Metric Metric Unit English Unit 1 liter 1.06 quarts gallon 1 quart 0.95 liter 1 gallon 3.78 liters 8

9 For more information 1. History of the International System of Units (SI) and Imperial Units: Bureau International des Poids et Mesures: National Institute of Standards and Technology: U.S. Metric Association: 2. s: Merriam-Webster: calculator: References for this lab material: www2.bakersfieldcollege.edu Tarbuck Lutgens 9