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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
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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. • Identifydifferent 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. • Usea 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) Countingobjects are always exact 2 soccer balls 4 pizzas Exact relationshipssuch as conversion factors 1 foot = 12 inches 1 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. counting 3. definition B. Measured numbers are obtained by 1. using a measuring tool 2. counting 3. 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)
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
What is the measure? What is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) 4.547 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 Error Meniscus
What is the level of uncertainty? • To what place value should we record an answer? • MUST look at INTERVAL • 17.6mL
Triple Beam Balance • Measures Mass • This tool measures in grams (g)
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.