Making MeasurementsMaking Measurements

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

Making MeasurementsMaking Measurements

• Why do we measure?

• What do we measure?

• 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

• 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)

• 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)

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

Systems of Measure:English (America)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

• 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)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

• 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 SystemMetric 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

• 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 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

• 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

• 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

• 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

• 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

• 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

• Gravity pulls equally on both sides of a balance scale, so you will get the same mass no matter what planet you are on

• 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

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

• 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

• 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!

• 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• 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).

• 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

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

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

• 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

• 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

• 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 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

• 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)

• 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

• 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

• 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 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?

• 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

To three significant digits:To three significant digits:

7.2327.232 7.237.23

7.230787.23078 7.237.23

7.2357.235 7.247.24

Rounding Off NumbersRounding 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

• 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 = 8.2152.65 x 3.1 = 8.215 8.2 8.2

Scientific NotationScientific 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?

• 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?

Scientific NotationScientific Notation

72377237 7.24 x 1037.24 x 103

Express in scientific notation:Express in scientific notation:

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