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Uncertainty in Measurements How to handle human measuring errors Choosing the Correct Piece of Equipment Every measuring device you use has a scale (lines) on it. Choosing the Correct Piece of Equipment The scale determines how precise your measurement will be. Choosing the Correct Piece of Equipment Your first step is always figuring out how much each line represents. Choosing the Correct Piece of Equipment What volume does each line represent on this graduated cylinder? Choosing the Correct Piece of Equipment 1 mL is correct! Reading a Graduated Cylinder Liquids in glass containers curve at the edges forming a… Reading a Graduated Cylinder Liquids in glass containers curve at the edges forming a… MENISCUS Reading a Graduated Cylinder Bend down to get eye level with and read the bottom of the MENISCUS Making a Measurement If a quantity falls between the lines on the scale, you must estimate some of the measurement Making a Measurement Estimating introduces human error into the measurement Reporting Your Measurement It is common practice to report all the “certain” digits (the ones you have a line for) 36 mL Reporting Your Measurement Plus one more decimal place beyond the scale 36.3 mL Reporting Your Measurement It is meaningless to report this level to the hundredths digit because you are already estimating at the tenths digits. 36.35 mL What is the Volume Here? 36.5 mL What is the Volume Here? 42.9 mL What is the Volume Here? 47.0 mL Be Careful What You Write Acceptable uncertainty is plus or minus “1” of the last digit recorded. Ex. 1.5 lbs. means the measurement is between 1.4 and 1.6 lbs. Ex. 1.500 lbs. means the measurement is between 1.499 and 1.501 lbs. This conveys a much more precise measurement!! Significant Figures All of the certain digits plus the first uncertain digit (the estimated number) are referred to as the Significant Figures of the measurement. Rules For Counting Significant Figures 1. Nonzero numbers are always significant. Ex. 32,127 has 5 sig.figs. Ex. 24 has 2 sig.figs. Rules For Counting Significant Figures 1. Nonzero numbers are always significant. 2. All numbers in scientific notation are significant. Ex. 6.02x1023 has 3 sig.figs. Ex. 1.392x10-5 has 4 sig.figs. Rules For Counting Significant Figures 3. Leading zeros (zeros that precede nonzero digits) are never significant. Ex. 0.0025 has 2 sig.figs. Ex. 0.7624 has 4 sig.figs. Rules For Counting Significant Figures 4. Captive zeros (zeros between nonzero digits) are always significant. Ex. 34,005 has 5 sig.figs. Ex. 10.00305 has 7 sig.figs. Ex. 0.002008 has 4 sig.figs. Rules For Counting Significant Figures 5. Trailing zeros (zeros at the end of the number) are sometimes significant. YES if you see a decimal point NO if you don’t see a decimal point. Ex. 2,000. has 4 sig.figs. Ex. 2,000 has 1 sig.fig. Ex. 2,000.00 has 6 sig.figs Rules For Counting Significant Figures 6. “Counting” numbers have an infinite number of significant figures Example 1: There are 20 students in the room. Example 2: Definitions…1 foot is exactly 12 inches How many significant figures? 0.0105 0.050080 8.050 X 10-3 20,200 Answers: 3, 5, 4,3 Handling Significant Figures in Mathematical Operations Uncertainty accumulates as calculations are carried out so we must follow a set of rules to handle significant figures when multiplying, dividing, adding, and subtracting numbers. I’m uncertain!! When Multiplying or Dividing Your answer can NOT have more sig. figs. than the least precise measurement Ex. 4.56 3 sig.figs. x 1.4 2 sig.figs. 6.384 can only have 2 sig.figs When Multiplying or Dividing Your answer can NOT have more sig. figs. than the least precise measurement Ex. 4.56 3 sig.figs. x 1.4 2 sig.figs. 6.384 can only have 2 sig.figs You are limited to 2 sig.figs. by the measurement 1.4, so you must round 6.384 to 6.4 When Multiplying or Dividing Your answer can NOT have more sig. figs. than the least precise measurement Ex. 4.56 3 sig.figs. x 1.4 2 sig.figs. 6.4 can only have 2 sig.figs You are limited to 2 sig.figs. by the measurement 1.4, so you must round 6.384 to 6.4 When Adding or Subtracting Your answer can’t have more places past the decimal than the least precise measurement Ex. 12.11 2 places past decimal + 18.0 1 place past decimal 1.013 3 places past decimal 31.123 can only have 1 place past decimal When Adding or Subtracting Your answer can’t have more places past the decimal than the least precise measurement Ex. 12.11 2 places past decimal + 18.0 1 place past decimal 1.013 3 places past decimal 31.123 can only have 1 place past decimal You must round answer to only 1 place past decimal When Adding or Subtracting Your answer can’t have more places past the decimal than the least precise measurement Ex. 12.11 2 places past decimal + 18.0 1 place past decimal 1.013 3 places past decimal 31.1 can only have 1 place past decimal You must round answer to only 1 place past decimal How to Round for Sig. Figs. Only look at the digit immediately to the right of the last significant figure – if less than 5, preceding digit stays the same – if 5 or more, round preceding digit up by one You Try It Round 4.348 to two sig. figs. These are the 2 sig figs You Try It Round 4.348 to two sig. figs. So look at the very next number for rounding It’s less than 5 so the 3 stays like it is Final Answer is 4.3

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posted: | 1/5/2013 |

language: | English |

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