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Measurement & Significant Figures

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

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  1. Measurement & Significant Figures Mrs. Page 2014-2015

  2. 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)

  3. 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

  4. 2 Types of Numbers • Exact • Measured

  5. 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

  6. 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.

  7. 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

  8. 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.

  9. 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)

  10. SI Units

  11. Important Prefixes

  12. Dimensional Analysis • Coming to a lesson soon

  13. 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

  14. What is the measure? What is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) 4.547 cm

  15. What is the measure in cm?

  16. Beaker • Measures Volume • This tool measures in milliliters (mL) • Not very accurate (what is the interval?)

  17. Conical (Erlenmeyer) Flask • Measures volume • Units – mL • Used when heating to avoid splashing and/or to collect gasses • Accurate???

  18. Graduated Cylinder • Measures Volume • Units – mL • Accurate???

  19. Reading a Graduated Cylinder Avoid Parallax Error Meniscus

  20. What is the level of uncertainty? • To what place value should we record an answer? • MUST look at INTERVAL • 17.6mL

  21. Reading a Graduated Cylinder

  22. Which Gives the MOST Accurate Measure? Why?

  23. Triple Beam Balance • Measures Mass • This tool measures in grams (g)

  24. Reading a Balance

  25. Electronic Scale • Measures mass in grams (g) • Digital equipment • Note all digits recorded • Uncertainty should be on equipment • Often must be calibrated

  26. BRAIN BREAK • http://brainbreaks.blogspot.com/2009/03/figure-eight-brain-break.html

  27. Significant Figures • Numbers that are important for performing calculations to ensure that your final answers are accurate • There are many significant figure rules

  28. THE RULES • All non-zero numbers are significant • Examples: • 65.23 • 4 sig. figs. • 23,456 • 5 sig. figs. • 1.234567 • 7 sig. figs

  29. 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.

  30. 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

  31. 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

  32. THE RULES • Significance of a DECIMAL point • MUST PAY ATTENTION • Try some more as Mrs. Page puts them on the board. • QUESTION???? ASK NOW!!!!

  33. 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)

  34. 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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