measurement & significant figures
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Measurement & Significant Figures. Mrs. Page 2014-2015. 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 - PowerPoint PPT PresentationTRANSCRIPT
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Measurement & Significant
Figures
Mrs. Page2014-2015
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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)
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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
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2 Types of Numbers– Exact– Measured
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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
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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.
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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
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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.
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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)
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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
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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
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Dimensional Analysis
• Coming to a lesson soon
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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
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What is the measure?
What is the length of the wooden stick?1) 4.5 cm 2) 4.54 cm 3) 4.547 cm
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What is the measure in cm?
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Beaker• Measures Volume• This tool measures in
milliliters (mL)• Not very accurate
(what is the interval?)
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Conical (Erlenmeyer) Flask
• Measures volume• Units – mL• Used when
heating to avoid splashing and/or to collect gasses
• Accurate???
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Graduated Cylinder
• Measures Volume• Units – mL• Accurate???
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Reading a Graduated Cylinder
Avoid Parallax ErrorMeniscus
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• What is the level of uncertainty?
• To what place value should we record an answer?
• MUST look at INTERVAL
• 17.6mL
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Reading a Graduated Cylinder
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Which Gives the MOST Accurate Measure? Why?
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Triple Beam Balance
• Measures Mass• This tool
measures in grams (g)
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Reading a Balance
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Electronic Scale
• Measures mass in grams (g)
• Digital equipment– Note all digits recorded– Uncertainty should be
on equipment– Often must be
calibrated
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BRAIN BREAK
• http://brainbreaks.blogspot.com/2009/03/figure-eight-brain-break.html
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Significant Figures
• Numbers that are important for performing calculations to ensure that your final answers are accurate
• There are many significant figure rules
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THE RULES
• All non-zero numbers are significant• Examples:
– 65.23 • 4 sig. figs.
– 23,456• 5 sig. figs.
– 1.234567 • 7 sig. figs
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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.
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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
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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
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THE RULES
• Significance of a DECIMAL point• MUST PAY ATTENTION• Try some more as Mrs. Page puts them on
the board.• QUESTION???? ASK NOW!!!!
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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)
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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.
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