Making Measurements

Making Measurements David A. Krupp, Ph.D. PaCES/HIMB Summer Program in Environmental Science

Making Measurements • Why do we measure? • What do we measure?

Variable • A feature or entity that can assume a value (observation) from a set of possible values (observations) • Some examples: • length of a rat tail • number of seeds in a seed pod • phosphate concentration of a water sample • color of a fish • ranking of how well you feel

Types of Variables • Quantitative variables • Continuous (e.g., length, weight, time, temperature) • Discontinuous (e.g., number of fish in an area, number of seeds in a seed pod; ) • Rank (e.g., one-to-five ranking for the quality of instruction) • Derived variables (e.g., density, velocity) • Character variables (e.g., color, gender)

Systems of Measure • Two systems in use predominantly: • English (America) • Metric or SI (European)

Systems of Measure:English (America) • Disadvantages • No standard base unit for each kind of measurement • Subunits within units not based upon a consistent multiplication factor • Difficult to make conversions between units • Advantages • We already know it

Systems of Measure:Metric or SI (European) • Disadvantages • We have to learn it • Advantages • Use a base unit for each type of measure • Subunits/superunits of base unit based upon multiples of ten • Conversions are much easier

Metric System • Developed by the French in the late 1700’s • Based on powers of ten, so it is very easy to use • Used by almost every country in the world, with the notable exception of the USA • Especially used by scientists • Abbreviated SI, which is French for Systeme International

Metric Prefixes • Regardless of the unit, the entire metric system uses the same prefixes • Common prefixes are: • kilo = 1000 • centi = 1/100th • milli = 1/1,000th • micro = 1/1,000,000th

Metric Prefixes • Example for length: • 1 meter (m) = 100 centimeters (cm) = 1,000 millimeters (mm) = 1,000,000 (m) • 1 kilometer (km) = 1000 meters

Length • Length is the distance between two points • The SI base unit for length is the meter • We use rulers or meter sticks to find the length of objects

Mass • Mass is the amount of matter that makes up an object • A golf ball and a ping pong ball are the same size, but the golf ball has a lot more matter in it. So the golf ball will have more mass • The SI unit for mass is the gram

Mass • A paper clip has a mass of about one gram • The mass of an object will not change unless we add or subtract matter from it

Measuring Mass • We could use a triple beam balance scale to measure mass • Gravity pulls equally on both sides of a balance scale, so you will get the same mass no matter what planet you are on

Weight • Weight is a measure of the force of gravity on an object • Your weight can change depending on the force of gravity • The gravity will change depending on the planet you are on • The SI unit for weight is the Newton (N) • The English unit for weight is the pound

Gravity • Gravity is the force of attraction between any two objects with mass • The force depends on two things: • Distance between the two objects • The mass of the two objects

Weight and Mass • Notice that Jill’s mass never changes. Her mother will not allow us to take parts off her, or add parts to her, so her mass stays the same. Jill is 30 kg of little girl no matter where she goes!

Volume • Volume is the amount of space contained in an object • We can find the volume of box shapes by the formula Volume = length x width x height • In this case the units would be cubic centimeters (cm3). • So a box 2 cm x 3 cm x 5 cm would have a volume of 30 cm3

Base Units • The base SI unit for volume is the Liter (L) • We normally measure volume with a graduated cylinder or a graduated pipette

Measuring Volumes • Liquids form curved, upper surfaces when poured into graduated cylinders • To correctly read the volume, read the bottom of the curve called the meniscus

Liquid Volume • When the metric system was created, they decided that 1 cm3 of water would equal 1 milliliter (mL) of water and the 1 mL of water will have a mass of one gram (g) • 1 cm3 water = 1 mL of water = 1 g

Water Mass and Volume • 1 cm3 water = 1 mL of water = 1 gram • So what would be the mass of 50 mL of water be? • 50 grams • So what would be the mass of 1 liter of water be? • 1 L = 1000 mL so its mass would be 1000 grams or a kilogram

Taking Measurements • All measurements include some degree of uncertainty • Sources of uncertainty • Instrument error • Calibration error • User error • A properly taken measurement includes one estimated digit (not always possible with digital readouts)

Taking Measurements • Measuring devices have units marked on them • When taking a measurement you record: • All known digits: those marked on the measuring device • One estimated digit: a multiple of 1/10 the smallest marked unit on the measuring device

Taking Measurements Value lies between 7.1 & 7.2 cm)

estimated digit Taking Measurements 7.16 cm

Accuracy Versus Precision • Accuracy • How close a measured value agrees with the true value • Precision • How closely repeated measurements agree with each other • Good measuring devices are both accurate and precise

Rounding Off Values • Generally should present values with the number of significant digits measured (including estimated digit) • Thus the value of 7.16 is presented to three significant digits • What would we present if we wished to round off our value to two significant digits?

7.237 7.24 Rounding Off Numbers To three significant digits: 7.232 7.23 7.23078 7.23 7.235 7.24

Rounding Off Numbers • General rule of thumb for presenting the number of significant digits for calculated values: • Use the number of significant digits of the value with the least significant digits 2.65 x 3.1 = 8.215  8.2

Scientific Notation • Goal: to express numbers in scientific notation and as ordinary decimal numbers • Scientific notation • A number between 1 and less than 10 multiplied by 10 raised to an exponent. • Examples: 1.63 x 105 2.1 x 103 5.341 x 10-4 • Why is scientific notation useful?

7237 Scientific Notation Express in scientific notation: 7.24 x 103 7000 7.0 x 103 345 3.45 x 102 0.351 3.51 x 10-1 0.0351 3.51 x 10-2

Making Measurements