Making MeasurementsMaking Measurements

David A. Krupp, Ph.D.David A. Krupp, Ph.D.BIOL 171L General Biology Lab IBIOL 171L General Biology Lab I

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

VariableVariable

• 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 VariablesTypes 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 MeasureSystems of Measure

• Two systems in use predominantly:–English (America)–Metric or SI (European)

• 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:English (America)

Systems of Measure:Metric or SI (European)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 PrefixesMetric 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 PrefixesMetric Prefixes

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

LengthLength

• 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

MassMass

• 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

MassMass

• 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 MassMeasuring Mass

• We could use a triple beam balance scale to measure mass

• It is unaffected by gravity

WeightWeight• 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

GravityGravity• 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

Jill Earth

1 gravity

Moon

1/6th gravity

Jupiter

2.5 gravities

On orbit

0 gravity

mass 30 kg 30 kg 30 kg 30 kg

weight 300 N 50 N 750 N 0 N

Weight and MassWeight 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!

VolumeVolume

• So a box 5 cm x 3 cm x 2 cm would have a volume of 30 cm3

• 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).

2 cm 5 cm

3 cm

Base UnitsBase Units

• The base SI unit for volume is the Liter (L)

• We normally measure volume with a graduated cylinder or a graduated pipette

Measuring VolumesMeasuring 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 VolumeLiquid 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

Pipette

Micropipette• Dial in volume

• 1st click- fill (slowly)

• Push to eliminate, 2nd click gets ride of last drop

• Use eject button to remove tip

Water Mass and VolumeWater 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 MeasurementsTaking 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 MeasurementsTaking 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 MeasurementsTaking Measurements

Value lies between 7.1 & 7.2 cm)

Value lies between 7.1 & 7.2 cm)

Taking MeasurementsTaking Measurements

7.16 cm7.16 cm

estimated digit

estimated digit

Accuracy Versus PrecisionAccuracy 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

Precise Accurate

Precise & Accurate

Rounding Off ValuesRounding 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?

Rounding Off NumbersRounding Off Numbers

7.2377.237 7.247.24

7.2327.232 7.237.23

7.230787.23078 7.237.23

7.2357.235 7.247.24

To three significant digits:

Rounding Off NumbersRounding Off Numbers

2.65 x 3.1 = 8.2152.65 x 3.1 = 8.215 8.2 8.2

• 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

Scientific NotationScientific Notation

Why is scientific notation useful?Why is scientific notation useful?

• 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

Scientific NotationScientific Notation

72377237 7.24 x 1037.24 x 103

70007000 7.0 x 1037.0 x 103

345345 3.45 x 1023.45 x 102

0.03510.0351 3.51 x 10-23.51 x 10-2

0.3510.351 3.51 x 10-13.51 x 10-1

Express in scientific notation:

Task for Today’s Lab Activity

•Practice using a pipette and eliminating waste properly.

•Practice using a micropipette.

Task for Today’s Lab ActivityTask for Today’s Lab Activity

• Work in pairs• Measure 20 koa haole, Leucaena

leucocephala, seed pods–length (nearest 0.1 cm)–weight (nearest (0.01 g)–number of seeds per pod

• Enter data into Excel spreadsheet

Task for Today’s Lab ActivityTask for Today’s Lab Activity

• Prepare single table in Excel that includes all measurement data and for length, weight and number of seeds per pod.

• Upload this table into your Dropbox on Laulima.