Measurement is the process of assigning numbers to quantities. It involves a quantity and a unit.
Measurement You are making a measurement when you • Check you weight • Read your watch • Take your temperature • Weigh a watermelon What kinds of measurements did you make today?
Where did it come from? Why 12 inches?
The King’s Foot One Foot
The King’s Foot One Foot Too big for some things...
Why 12 inches not 10 or 13? Simply because it took 12 lengths of his first knuckle to equal his foot.
...So they used the length of the King’s first knuckle One Inch But that was too big for some other things...
...That’s exactly how they made inches. the fractions between the 1/2 1/4
...So they cut the inches into fractions 1/2 1/4 1/8 and 1/16
You should have noticed that as the fractions got smaller, so did the length of the lines between the whole numbers. That helps to identify a half from the fourths and so on.
If you don’t remember what the fraction is just by looking at the ruler, you can always count the number of lines between the whole numbers. If there are 16, then your ruler is divided into sixteenths.
If you counted 10 lines from the whole number, that would be 10 sixteenths. Here’s where that “magic number 2” comes in. To get the fraction to it’s lowest possible denominator DIVIDE both numbers in the fraction by 2 and keep doing it until the top number is odd. 10 = 5 Top number’s odd so 10/16 = 5/8 16 8 If the fraction comes between two whole numbers like 1 and 2, then the measurement is the first whole number and the fraction in this case it would be 1 and 5/8ths ..then you can do the math to determine the fraction.
Name this measurement • A. 1/2 • B. 1/3 • C. 1/4 • D. 5/16
Name this measurement • A. 3/4 • B. 3/8 • C. 1-3/4 • D. 2-3/4
The Metric ruler is much different. Everything is based on 10 10mm (millimeters) = 1cm (centimeter) 100cm= 1m (meter) 1m = 100cm (cm = centimeter, cent means 100) 1m = 1000mm (mm = millimeter, mil means 1000)
This is a magnified image of a ruler/meter stick. 1 2 3 4 This is half of a centimeter.
This is a magnified image of a ruler/meter stick. 1 2 3 4 This is one millimeter.
English Base Units • For measuring length a yard is used and one yard = 0.914 meters • An inch is used for measuring the length of smaller objects and 1inch = 2.54 cm
English Base Units • For measuring mass the pound is used and one pound = 0.45 kilograms
English Base Units • An ounce is used for measuring the mass of smaller objects and 1 ounce = 28.35 grams.
English Base Units • For measuring volume a gallon is used and 1 gallon = 3.78 liters
English Base Units • A fluid ounce (oz.) is used to measure the volume of smaller objects and 1 fluid ounce = 29.6 milliliters
Metric System • The metric system is based on a base unit that corresponds to a certain kind of measurement • Length = meter • Volume = liter • Weight (Mass) = gram • Prefixes plus base units make up the metric system • Example: • Centi + meter = Centimeter • Kilo + liter = Kiloliter
Metric System • The three prefixes that we will use the most are: • kilo • centi • milli
Metric System • So if you needed to measure length you would choose meter as your base unit • Length of a tree branch • 1.5 meters • Length of a room • 5 meters • Length of a ball of twine stretched out • 25 meters
Metric System • But what if you need to measure a longer distance, like from your house to school? • Let’s say you live approximately 10 miles from school • 10 miles = 16093 meters • 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: • 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)
Metric System • These prefixes are based on powers of 10. What does this mean? • From each prefix every “step” is either: • 10 times larger or • 10 times smaller • For example • Centimeters are 10 times larger than millimeters • 1 centimeter = 10 millimeters
Metric System • Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length 1 centimeter = 10 millimeters Example not to scale 40 41 40 41 1 cm
Metric System • For each “step” to right, you are multiplying by 10 • For example, let’s go from a base unit to centi 1 liter = 10 deciliters = 100 centiliters 2 grams = 20 decigrams = 200 centigrams ( 1 x 10 = 10) = (10 x 10 = 100) (2 x 10 = 20) = (20 x 10 = 200)
Metric System • An easy way to move within the metric system is by moving the decimal point one place for each “step” desired Example: change meters to centimeters 1 meter = 10 decimeters = 100 centimeters or 1.00 meter = 10.0 decimeters = 100. centimeters
Metric System • Now let’s try our previous example from meters to kilometers: 16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers • So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)
Metric System • If you move to the left in the diagram, move the decimal to the left • If you move to the right in the diagram, move the decimal to the right
Metric System • Now let’s start from centimeters and convert to kilometers 400000 centimeters = 4 kilometers 400000 centimeters = 4.00000 kilometers
Metric System • Now let’s start from meters and convert to kilometers 4000 meters = 4 kilometers • Now let’s start from centimeters and convert to meters • 4000 centimeters = 40 meters
Metric System • Now let’s start from meters and convert to centimeters 5 meters = 500 centimeters • Now let’s start from kilometers and convert to meters • .3 kilometers = 300 meters
Metric System • Now let’s start from kilometers and convert to millimeters 4 kilometers = 4000000 millimeters or 4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = 400000 centimeters = 4000000 millimeters
Metric System • Summary • Base units in the metric system are meter, liter, gram • Metric system is based on powers of 10 • For conversions within the metric system, each “step” is 1 decimal place to the right or left • Using the diagram below, converting to the right, moves the decimal to the right and vice versa
Systems of Measurement • Why do we need a standardized system of measurement? • Scientific community is global. • An international “language” of measurement allows scientists to share, interpret, and compare experimental findings with other scientists, regardless of nationality or language barriers. • By the 1700s, every country used its own system of weights and measures. England had three different systems just within its own borders!
Metric System & SI • The first standardized system of measurement: the “Metric” system • Developed in France in 1791 • Named based on French word for “measure” • based on the decimal (powers of 10) • Systeme International d'Unites(International System of Units) • Modernized version of the Metric System • Abbreviated by the letters SI. • Established in 1960, at the 11th General Conference on Weights and Measures. • Units, definitions, and symbols were revised and simplified.
UNIT CONVERSIONS • Quantities can be converted from one type of unit to another. This conversion may occur within the same system (metric or English) or between systems (metric to English or English to metric). • Conversions cannot be made between measures of different properties, that is, mass units to length units for example. • A method of unit conversion commonly used is called Dimensional Analysis or Unit Analysis. In this procedure, units are used to decide when to multiply or divide in order to obtain the correct answer.
Unit Analysis Problem Solving Procedure Step 1 : 2.35 Kg ? g Step 2 : FROM THE CONVERSION TABLE 1000 g / kg Step 3 : CANCEL UNITS TO LEAVE UNITS OF THE ANSWER x ( 1000g/ Kg ) 2.35Kg Perform the operations Step 4 : ( 2.35Kg) ( 1000 g/ 1 Kg ) 2 350 g x =
Dimensional/ Unit Analysis – metric to metric 1. How many meters are contained in 800cm? 800 cm m 800 cm x 1 m = 800 = 8 m 100 cm 100 2. How many Kg are there in 1200 g? 1200g Kg 1200 g x 1Kg = 1200 = 1.2 Kg 1000 g 1000
Dimensional/Unit Analysis – English metric 1. How many grams are contained in 25 lbs? 25 lbs g 25 lbs x 1Kg x 1000g = 25 000 2.2 lbs 1 Kg 2.2 =11 363.63 g 2. How many pounds are there in 75 Kg? 75Kg lbs 75 Kg x 2.2 lbs = 165 lbs 1 Kg