Technical Science Scientific Tools and Methods

Technical ScienceScientific Tools and Methods The Metric System

The Metric System • In this section you will … • Describe the features of a measurement system • Describe the benefits of the Metric System • Make metric conversions • Make metric measurements

1 of 7 Measurement Systems Home • Any measurement system will have three features. • Standard Units • Additional units for measuring large and small quantities • Relationships between units of measure

2 of 7 Measurement Systems • Standards are units of measure that are the same no matter where you go. • A foot represents the same distance everywhere in the US. A foot is a standard unit of length. • Since everyone agrees on the value of a standard, they insure that measurements are consistent.

3 of 7 Measurement Systems • You will want to make other measurements besides length. A standard is necessary for each type of measure you want to make. Measurement English Metric Length Foot Meter Weight Pound Gram Capacity Gallon Liter etc etc etc

4 of 7 Measurement Systems • A foot is a standard unit of length. But, it is not a good unit for measuring all lengths. • You could measure the room or a table in feet. But it would not make sense to measure a blood cell or the distance between two cities in feet. • A measurement system must have additional units to measure very large and very small amounts.

5 of 7 Measurement Systems • What are some of the additional units of measure for length, weight, and capacity in the English system? Length Inch, Foot, Yard, Mile, etc Weight Ounce, Pound, Ton, etc Capacity Cup, Pint, Quart, Gallon, Barrel, etc

6 of 7 Measurement Systems • Finally, measurement systems must have relationships between the units of measure. • Since inches, feet, yards, and miles are all measurements of length then you should be able to convert from one to another. • There are 12 inches in one foot. There are 3 feet in one yard. There are 1760 yards in a mile. These relationships are constant. This allows us to convert from one unit to another.

7 of 7 Measurement Systems Home • What are the three requirements for a measurement system? • There must be standards for every type of measurement you want to make. • There must be additional units for measuring large and small quantities. • There must be a relationship between the units of measure.

1 of 11 Benefits of the Metric System Home • Any measurement system will have three features • Standard Units • Additional units for measuring large and small quantities • Relationships between units of measure • If both the English system and the Metric system have all the requirements for a measuring system, why should we switch to the metric system? • To answer this question, let’s see how convenient the English system is to work with.

2 of 11 Benefits of the Metric System • Let’s say you were asked the following question: How many inches are in one mile? • To answer this question you would need some of the information that follows. • 12 inches = 1 foot 3 feet = 1 yard • 5280 feet = 1 mile 1760 yards = 1 mile • Now you can see one problem with the English system. There is no consistent relationship between the units in the English system.

3 of 11 Benefits of the Metric System • There is no consistent relationship between the units in the English system. • There are 12 inches in 1 foot. There are 3 feet in 1yard and there are 5280 feet in 1 mile. • This inconsistency makes converting in the English system very difficult for two reasons. • You have to remember all those different conversions. • Calculating with those peculiar numbers can be time consuming even with a calculator.

4 of 11 Benefits of the Metric System • The Metric system has a consistent relationship between units. • This means that as you move from one unit to the next larger or smaller you always change by the same factor. • In the Metric system the factor by which you change is 10. This makes the Metric system a base-ten system. • The next slides will explain this in more detail.

5 of 11 Benefits of the Metric System • Our monetary system is an example of a familiar base-ten system. Dollar <=> Dime <=> Penny • As you go from one unit to the next larger or smaller, you are changing by a factor of ten. • 10 pennies = 1 dime 10 dimes = 1 dollar. • 1 penny = 0.1 dimes 1 dime = 0.1 dollars

6 of 11 Benefits of the Metric System • Converting between units in a base ten system is very easy. Dollar <=> Dime <=> Penny • To convert from a unit to the next smaller unit, multiply by 10 • 2 dollars = 20 dimes (2 x 10 = 20). • 5 dimes = 50 pennies (5 x 10 = 50) • To convert from a unit to the next larger unit, divide by 10. • 30 pennies = 3 dimes (30  10 = 3) • 60 dimes = 6 dollars (60  10 = 6)

7 of 11 Benefits of the Metric System • What if you had to convert from pennies to dollars or dollars to pennies? Dollar <=> Dime <=> Penny • Dollars and Pennies are “two positions” apart. • Each position change represents a factor of 10. • 2 positions are 2 factors of 10 or 100 (10 x 10 = 100) • Multiply to convert from a larger to a smaller unit. • 3 dollars = 300 pennies (3 x 100 = 300) • Divide to convert from a smaller to a larger unit. • 700 pennies = 7 dollars (700  100 = 7)

8 of 11 Benefits of the Metric System • Converting in a base ten system is just a matter of multiplying or dividing by a factor of 10. (Factors of 10 = 10, 100, 1000, 10,000 etc.) • A fast way to multiply or divide by a factor of ten is to move the decimal. 5.623 x 100 = 5 6 2 3 . . . 45.92  10 = 4 5 9 2 . . • Multiply by 100, move the decimal 2 places to the right • Divide by 10, move the decimal 1 place to the left • Since the Metric System is base ten, you can convert units by simply moving the decimal point.

9 of 11 Benefits of the Metric System • Another benefit of the Metric System is the fact that that the whole world uses it. (except the US) • In order for a measurement system to be useful everyone must agree on the standards that make it up. • The more people that agree on those standards the better the system will be. • All fields of science use only the Metric System.

10 of 11 Benefits of the Metric System • You might be wondering: If the Metric system is so great why don’t we use it in the US. • The truth is that we do use the metric system. • You have probably bought a 2 liter bottle of soda • Your car has many metric parts • The aspirin you take is measured in milligrams. • The US is in the middle of a very slow process of converting to the Metric system. • As time goes by, the metric system will become a bigger part of your life.

11 of 11 Benefits of theMetric System Home • Why should US companies be concerned about switching to the Metric System? • If they want to sell products to other countries they have to use their standards of measure. • It is probably more expensive to use two different measurement systems. • If some parts are produced in another country will they be compatible with parts produced here?

1 of 11 Making Metric Conversions Home • Study the table below to become familiar with metric units of measure. Back

2 of 11 Making Metric Conversions • Answer the following questions. Use the button below to refer to the Table of Metric Prefixes. • What is the base unit of measure for ... • Length = • Mass = • Volume = • Meter • Gram • Liter Table

3 of 11 Making Metric Conversions • Name the following units of measure. Use the prefix followed by the base unit. • 1,000 meters = • 0.001 liters = • 0.000001 grams = • 0.01 meters = • 10 gram = • 1,000,000 bytes = • Kilometer • Milliliter • Microgram • Centimeter • Dekagram • Megabyte Table

4 of 11 Making Metric Conversions • You probably noticed that the metric prefixes stay the same no matter what unit of measure you use. • Length in the English system is measured in inches, feet, yards, miles etc. but volume is measured in ounces, cups, quarts, gallons, etc. • In the metric system kilo is always 1,000 base units. It doesn’t matter what you are measuring. • 1000 grams is akilogram. 1000 watts is a kilowatt. • There are a lot less metric units to remember. • This is another benefit of the Metric System. Table

5 of 11 Making Metric Conversions • Name the unit when given the abbreviation and vice versa. Metric abbreviations use small case letters (except mega and giga) and no periods. • km = Mililiter = • mg = Kilogram = • cm = Nanometer = • Mg = Decimeter = • ug = Dekagram = • Kilometer • Milligram • Centimeter • Megagram • Microgram • ml • kg • nm • dm • dkg Table

6 of 11 Making Metric Conversions • Now that you are familiar with metric units, you can make some conversions. • To make conversions within the Metric System, you have to answer two questions. • First, how many positions is it from the starting unit to the unit you want to convert to? Since the metric system is base ten, this tells how many places to move the decimal. • Second, are you converting from a larger unit to a smaller unit or from a smaller unit to a larger unit? This tells which way to move the decimal.

7 of 11 Making Metric Conversions • 4.5 kilometers = meters. 4 5 0 0 . . . . • It is 3 positions from the starting unit (kilo) to the unit we want to convert to (base unit - meter). • We are converting from a larger unit to a smaller unit. • We need more small units than large units to make up the same amount of distance. • This means moving the decimal three places to the right.

8 of 11 Making Metric Conversions • 8.3 milligrams = micrograms. 8 3 0 0 . . . . • It is 3 positions from the starting unit (milli) to the unit we want to convert to (micro). • We are converting from a larger unit to a smaller unit. • We need more small units than large units to make up the same amount of mass. • This means moving the decimal three places to the right. • Note: the dashed lines represent positions. From milli to micro is 3 positions not 1

9 of 11 Making Metric Conversions . . • 25,000 centimeters = kilometers. . . . 0 . 2 5 0 0 0 • It is 5 positions from the starting unit (centi) to the unit we want to convert to (kilo). • We are converting from a smaller unit to a larger unit. • We need fewer large units than small units to make up the same amount of distance. • This means moving the decimal five places to the left.

10 of 11 Making Metric Conversions • 75 milliliters = liters 0 . 0 . 7 5 . . • It is 3 positions from the starting unit (milli) to the unit we want to convert to (base unit - liter). • We are converting from a smaller unit to a larger unit. • We need fewer large units than small units to make up the same amount of volume. • This means moving the decimal three places to the left.

11 of 11 Making Metric Conversions Home • Make the following metric conversions. • 1,000 grams = kg • 500 mg = g • 2.25 liters = ml • 0.07 g = kg • 1 kilometer = m • 450 ul = ml • 75 cm = um • 650 cm = m • 0.30 kg = mg • 1 • 0.5 • 2250 • 0.00007 • 1000 • 0.450 • 750,000 • 6.5 • 300,000 Table

1 of 24 Making MetricMeasurements Home • Now you can make metric conversions but can you answer the questions below? • You need 5 kilograms of potatoes from the store, can you carry them or should you take your car? • A label on a bottle of cough syrup reads give 5 milliliters as needed. Will 5 milliliters fit in a teaspoon or will you need a tablespoon? • You are running a 1600 meter race. Is this a sprint or a distance event?

2 of 24 Making MetricMeasurements • Using the metric system isn’t just about converting. You need to have a “feel” for the size of units you are working with. • The English system is familiar to you. You have an idea about how heavy 5 pounds is but you probably don’t have that same feeling for 5 kilograms. • The best way to get familiar with the metric system is to use it to make measurements.

3 of 24 Making MetricMeasurements - Length • The following are approximations to help you get a feel for metric units of length. We will deal only with the most common units. • 1 kilometer  Just over one half mile • 1 meter  Just over one yard • 1 centimeter  Width of your little fingernail • 1 millimeter  Thickness of your fingernail • 1 micrometer  Diameter of a bacteria

4 of 24 Making MetricMeasurements - Length • Choose the most appropriate measure. • Length of a football field • 1 km, 100 m, 1,000 um, 10 cm, 100 mm • Length of a newborn baby • 0.5 m, 0.05 km, 500 um, 5,000mm, 50 cm • Thickness of a sheet of paper • 0.1 mm, 0.1 cm, 0.01 m, 1 km, 10 um

96 97 98 99 1 m 1 2 3 4 5 of 24 Making Metric Measurements - Length • The diagram below is part of a metric tape measure. The numbered divisions are centimeters. The small divisions are millimeters • How many millimeters are in 1 cm? • How many centimeters are in 1 m? • Is the diagram drawn to scale? • Are the units too large or too small? • 10 Millimeters • 100 Centimeters • No • Too large

96 97 98 99 1 m 1 2 3 4 6 of 24 Making Metric Measurements - Length A • Measure Line A in mm, cm, and m. (Hint: make your initial measurement in mm then convert.) • You have gone 99 cm and 2 mm. • 99 cm = 990 mm • + 2 mm • 992 mm => • 99.2 cm => • 0.992 m

96 97 98 99 1 m 1 2 3 4 7 of 24 Making Metric Measurements - Length B • Measure Line B in mm, cm, and m. • You have gone 1 m, 2 cm, and 7 mm. • 1m = 100 cm = 1000 mm • 2 cm = 20 mm • + 7 mm • 1027 mm => • 102.7 cm => • 1.027 m

96 97 98 99 1 m 1 2 3 4 8 of 24 Making Metric Measurements - Length 1 2 • Measure Line 1 and 2 in mm, cm, and m. • Line 1 = • Line 2 = • 1004 mm => • 100.4 cm => • 1.004 m • 979 mm => • 97.9 cm => • 0.979 m

96 97 98 99 2 m 1 2 3 4 9 of 24 Making Metric Measurements - Length 3 4 • Measure Line 3 and 4 in mm, cm, and m. • Line 3 = • Line 4 = • 2015 mm => • 201.5 cm => • 2.015 m • 1998 mm => • 199.8 cm => • 1.998 m

10 of 24 Making MetricMeasurements - Mass • The following are approximations to help you get a feel for metric units of mass. We will deal only with the most common units. • 1 kilogram  Just over 2 pounds • 1 gram  Mass of a raisin • 1 milligram  Mass of a grain of sand

11 of 24 Making MetricMeasurements - Mass • Choose the most appropriate measure. • Mass of a nickel • 50 g, 5 mg, 0.5 kg, 5 g, 500 mg • Mass of an aspirin • 500 mg, 0.5 mg, 500 g, 50 kg, 50 g • Mass of an average adult • 700 kg, 0.7 g, 700 mg, 7,000 g, 70 kg • Mass of a baseball • 400 mg, 0.4 g, 4 kg, 400 g, 40 g

? 20g 10g 50g 12 of 24 Making Metric Measurements - Mass • Mass is measured using a balance. The object to be measured is placed in one pan and standard mass units are placed in the other pan. • How many milligrams are in 1 g? • How many grams are in 1 kg? • 1000 Milligrams • 1000 Grams

A 20g 10g 50g 13 of 24 Making Metric Measurements - Mass • Measure Object A in g, mg, and kg. • Put standard mass units in the pan until it balances. • 50 g • + 20 g • + 10 g • 80 g => • 80,000 mg => • 0.080 kg

B 10g 50g 50g 14 of 24 Making Metric Measurements - Mass • Measure Object B in g, mg, and kg. • Put standard mass units in the pan until it balances. • 50 g • + 50 g • + 10 g • 110 g => • 110,000 mg => • 0.110 kg

1 20g 10g 50g 50g 15 of 24 Making Metric Measurements - Mass • Measure Object 1 in g, mg, and kg. • Put standard mass units in the pan until it balances. • 0.130 kg • 130,000 mg => • 130 g => • Object 1 =

2 10g 50g 16 of 24 Making Metric Measurements - Mass • Measure Object 2 in g, mg, and kg. • Put standard mass units in the pan until it balances. • 0.060 kg • 60,000 mg => • 60 g => • Object 2 =

17 of 24 Making MetricMeasurements - Volume • The following are approximations to help you get a feel for metric units of volume. We will deal only with the most common units. • 1 liter  Just over 1 quart • 1 milliliter  About 20 drops

18 of 24 Making MetricMeasurements - Volume • Choose the most appropriate measure. • Volume of a car’s gas tank • 50 l, 5 l, 500 ml, 50 ml, 500 l • Volume of a teaspoon • 0.5 l, 0.5 ml, 5 l, 5 ml, 500 ml • Volume of a can of soda • 500 l, 0.05 l, 500 ml, 0.5 ml, 0.005 ml • Volume of a syringe • 0.02 ml, 200 ml, 0.02 l, 2 l, 2 ml

1000 ml 750 ml 100 ml 500 ml 200 ml 50 ml 250 ml 100 ml 19 of 24 Making Metric Measurements - Volume • Volume can be measured using beakers that are designed to hold a standard amount of fluid. • How many milliliters are in 1 liter? • Do the small divisions represent the same volume on each beaker? • 1000 Milliliters • False

Technical Science Scientific Tools and Methods