Download - Measurement & Significant Figures
Measurement & Significant
Figures
Mrs. Page2014-2015
By the end of this lesson you should be able to:
• Distinguish between exact and measured numbers.
• Identify different pieces of lab equipment, what it measures & the units of measurement
• State the SI units for mass, length, volume, temperature, and amount of a substance.
• Use a ruler, graduated cylinder, triple beam balance to make accurate measurement (to correct place value)
By the end of this lesson you should be able to:
• Explain how a measured number tells the audience about the accuracy of the tool used to make a measurement
• Determine the number of significant figures in a given number
• Perform calculations & express solutions with correct number of significant figures
2 Types of Numbers– Exact– Measured
Exact Numbers (3 types)Counting objects are always exact
2 soccer balls4 pizzas
Exact relationships such as conversion factors1 foot = 12 inches1 meter = 100 cm
Constants/ By DefinitionPi, Avogadro’s #, speed of light
Measured Numbers• Measured numbers will always include
some degree of ERROR• An instrument is used for measuring and
therefore the user must at some point estimate the value.
• When you use your calculator to calculate using a measured number your answer can only be as accurate as your worst measurement.
Learning Check
A. Exact numbers are obtained by 1. using a measuring tool
2. counting3. definition
B. Measured numbers are obtained by 1. using a measuring tool
2. counting3. definition
Learning Check
Classify each of the following as an exact or a
measured number.
1 yard = 3 feet
The diameter of a red blood cell is 6 x 10-4 cm.
There are 6 hats on the shelf.
Gold melts at 1064°C.
Metric System• Every measurement has 2 parts:
– Number– Unit (scale)
• SI System (le Systeme International) is based on the metric system
• Prefix + Base Unit • Prefix tells you the power of 10 to multiply
by (easy for conversions)
SI UnitsMeasuring Base Unit Symb
olMass Kilogram kgVolume (solid) (liquid)
Cubic centimeterLiter
cm3L
Length Meter mTime Second sTemperature Kelvin KAmount of Substance Moles molForce Newton N
Important PrefixesPrefix Symbol Amount Scientific
Notation
Giga - G 1,000,000,000 109
Mega - M 1,000,000 106
Kilo - k 1,000 103
Deci d 0.1 10-1
Centi - c 0.01 10-2
Milli - m 0.001 10-3
Micro - µ 0.000001 10-6
Nano- n 0.000000001 10-9
Dimensional Analysis
• Coming to a lesson soon
Tool: Ruler• Measures length• Measures in centimeter (cm)
• All measurements have a degree of uncertainty!• We can see the markings between 1.6-1.7cm• We can’t see the markings between the 0.6-0.7• We must “guess” between 0.6 & 0.7• We record 1.67 cm as our measurement• The last digit an 7 was our guess...stop there
1 2 3 4 cm
What is the measure?
What is the length of the wooden stick?1) 4.5 cm 2) 4.54 cm 3) 4.547 cm
What is the measure in cm?
Beaker• Measures Volume• This tool measures in
milliliters (mL)• Not very accurate
(what is the interval?)
Conical (Erlenmeyer) Flask
• Measures volume• Units – mL• Used when
heating to avoid splashing and/or to collect gasses
• Accurate???
Graduated Cylinder
• Measures Volume• Units – mL• Accurate???
Reading a Graduated Cylinder
Avoid Parallax ErrorMeniscus
• What is the level of uncertainty?
• To what place value should we record an answer?
• MUST look at INTERVAL
• 17.6mL
Reading a Graduated Cylinder
Which Gives the MOST Accurate Measure? Why?
Triple Beam Balance
• Measures Mass• This tool
measures in grams (g)
Reading a Balance
Electronic Scale
• Measures mass in grams (g)
• Digital equipment– Note all digits recorded– Uncertainty should be
on equipment– Often must be
calibrated
BRAIN BREAK
• http://brainbreaks.blogspot.com/2009/03/figure-eight-brain-break.html
Significant Figures
• Numbers that are important for performing calculations to ensure that your final answers are accurate
• There are many significant figure rules
THE RULES
• All non-zero numbers are significant• Examples:
– 65.23 • 4 sig. figs.
– 23,456• 5 sig. figs.
– 1.234567 • 7 sig. figs
THE RULES
• All zeros between two non-zero numbers are significant
• Examples:– 2014
• 4 sig. figs
– 300,002• 6 sig. figs
– 1.0005• 5 sig. figs.
THE RULES
• Place holder zeros are NOT significant – Leading zero - before any digits
• 0.0012 – 2 sig. figs
– Trailing zeros – after digits but BEFORE a decimal • 345,000
– 3 sig. figs
• 41,980,000.– 4 sig. figs
THE RULES
• All zeros at the end of a number and AFTER the decimal point are significant
• Examples:– 5.0000
• 5 sig figs
– 402.0• 4 sig figs
– 0.450• 3 sig figs
THE RULES
• Significance of a DECIMAL point• MUST PAY ATTENTION• Try some more as Mrs. Page puts them on
the board.• QUESTION???? ASK NOW!!!!
Calculations w/ Sig. Figs.RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers. (answer has # of sig. figs of smaller # of sig figs)
Calculations w/ Sig. Figs.RULE 2. In carrying out an addition or subtraction, the answer cannot have more digits after the decimal point than either of the original numbers.