Intro to Measurement

Isn’t it just reading the ruler?

Objectives

• Explain why numbers need units• List the seven SI base units and explain

what they are used to measure• Explain how SI base units are defined• Explain the difference between a base unit

and a derived unit• Read any measuring device to the proper

degree of precision• Explain the difference between accuracy

and precision

History of Measurement

• The English units that we use in the United States developed over a long time. For example, the hand was devised in ancient times as a unit of length. It was defined as the length of a person’s hand from the little finger to the thumb.

• Today the height of horses is still measured in hands, but the definition of a hand is standardized at 4 inches or 10.16 centimeters.

Where do the numbers come from?

• The numbers used in science class are measurements of some aspect of the universe

• What does this require?

– A system to make sure everybody measures the same thing the same way

SI System

• A system agreed upon by scientists to produce consistency in measurement

• Based on some aspect of the physical universe that is easily verified and always constant– Length: The distance light travels in a

certain amount of time– Time: The amount of time it takes for a

molecule to “vibrate” a certain number of times

Base Units vs. Derived Units

• Base Units are the fundamental measurements that we use to describe an object

• Derived Units are a combination of two or more base units– Some things can’t be described by only

one unit– Ex: Speed measures the distance you

travel and the amount of time it takes to travel that distance (meters per second)

SI Base UnitsLength Meter m

Mass gram g

Temperature Kelvin K

Time Second s

Amount of Substance

Mole mol

Electric Current Ampere A

Brightness Candela cd

Why Units?

• Units are required on (almost) EVERY number that we use in science class

• Remember, numbers are measurements

• What is it exactly that you are measuring?

– Units will tell you this!!

SI Prefixes

• Kilo = 1,000 Hecto = 100 Deka = 10

• Deci = .1 Centi = .01 Milli = .001

K H Da B D C M

Conversion Factors

• Conversion factors are fractions that equal 1

• Ex) 1 minute / 60 seconds

• 12 months / 1 year 1,000 meters / 1 kilometer

• 100 centigrams / 1 gram 100 liters / 1 hectoliter

Dimensional Analysis

• The use of conversion factors to change units

• 20 Kg = ??? G

– 20 kg / 1 X 1,000 g / Kg = 20,000 g

Practice problems

• 10 Hm = ________ Km

• 1 m = __________ Km

• 5 Hg = __________ cg

• 3,000 mL ________ L

• 40 dm = _________ dam

• 1.9 cg = _________ g

• 300 mm = _________ dm

Practice problems

• ________ m = 234 Km

• ________ daL = 1.2 cL

• ________ kg = 36.54 dg

• ________ mg = 14.8 g

• ________ KL = 439 L

• ________ g = .5 Kg

• ________ mL = 456 cm3

Derived Measurements

• Volume can be derived or direct dependent on the tools used in measurement

• Ex. - using a graduated cylinder = direct

• Ex. – using a ruler to measure length, width and height is derived

Area and Volume formulas

• Appendix A, Page 830

cube = a 3 rectangular prism = a b c irregular prism = b h cylinder = b h = pi r 2 h pyramid = (1/3) b h cone = (1/3) b h = 1/3 pi r 2 h sphere = (4/3) pi r 3

How to Measure

• Certain Digit: What part of the measurement do you know FOR SURE!!

• Uncertain Digit: What is your best guess as to the actual value of the measurement

• No measurement is exact – they are only as good as the tools we use and the person using those tools

Meniscus Madness

http://www.morrisonlabs.com/meniscus.htm

How to Measure

1 cm

2 cm

3 cm

4 cm

5 cm

6 cm

7 cm

8 cm

9 cm

10 cm

We know FOR SURE that the line is between 5 cm

and 6 cm, therefore, we have one

CERTAIN DIGIT:

5.?

It looks to me that the line is about 70% (or 7/10) of the way from

the 5 cm line to the 6 cm line. We now have one

UNCERTAIN DIGIT

5.7 cm

Certain vs. Uncertain Digits

• The number of CERTAIN digits will vary, depending on the measuring tool used

• There will ALWAYS be only one uncertain digit, which is an estimation of how far between the last certain digit and the next certain digit the actual measurement is

How to Measure

7.1 cm

7.2 cm

7.3 cm

7.4 cm

7.5 cm

7.6 cm

7.7 cm

7.8 cm

7.9 cm

8.0 cm

8.1 cm

We know FOR SURE that the line is

between 7.7 cm and 7.8 cm, therefore, we have TWO CERTAIN

DIGITS:

7.7?

It looks to me that the line is about 20% (or 2/10) of the way from

the 7.7 cm line to the 7.8 cm line. We now have

one UNCERTAIN DIGIT

7.72 cm

How to Measure

7.1 g

7.2 g

Each line represents 0.01 g

Definitely between 7.10g and 7.11g, so 7.10?

About 50% of the way, so 7.105 g

Looks to be almost exactly on the 7.16 g line

7.160 g

Accuracy vs. Precision

• Accuracy is the closeness of a measured value to the ACTUAL value

• Precision is the closeness of a bunch of measured values to each other

• “Incorrect Ruler” Scenario

– Measurements would be precise, but not accurate

Percent Error

• The percent error between a known quantity and an experimental or estimated quantity is found by:

• E – A / A * 100 = % Error

• ( the parallel lines mean “absolute value”)