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Measuring, Rounding, and Calculation Rules

Measuring, Rounding, and Calculation Rules. Chemistry Question: What is the volume of water in the graduated cylinder in mL ? How many sigfigs is this? How many L is this? Express this number in sci. notation. Measuring with SigFigs.

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Measuring, Rounding, and Calculation Rules

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  1. Measuring, Rounding, and Calculation Rules

  2. Chemistry Question: • What is the volume of water in the graduated cylinder in mL? • How many sigfigs is this? • How many L is this? • Express this number in sci. notation.

  3. Measuring with SigFigs • Always take the measurement to one decimal place past the smallest gradation (tic mark) • Graduated cylinders • Beakers/flasks/bottles /etc. are NOT used for measuring! Measure the volume of liquids ONLY with a graduated cylinder • Rulers • When using the electronic balance, record the entire number on the screen

  4. 66.2 mL

  5. 12.80 mL

  6. 21.75 mL

  7. 2.65 cm

  8. 3.53 cm

  9. Rounding Numbers • Rules for rounding to the correct number of sig-figs: • For numbers greater than five, round up as you normally would: • Round to 3 sig-figs: 4.287 4.29

  10. Rounding Numbers • For numbers less than five, round down as you normally would: • Round to 3 sig-figs: 4.284 4.28

  11. Rounding Numbers • For fives with non-zero digits after them, round up • Round to 3 sig-figs: 4.2857 4.29

  12. Rounding Numbers • For fives with zeroes after them, “round even” • Round to 3 sig-figs: 4.285 4.28 4.275  4.28

  13. Adding/Subtracting with SigFigs • When adding or subtracting: • The answer must have the same number of digits to the right of the decimal point as the measurement with the fewest digits to the right of the decimal point. • 21.5 + 23.56 + 29.541 =

  14. Adding/Subtracting with SigFigs • 21.5 + 23.56 + 29.541 = • = 74.601 • 21.5 only has one decimal place, so our answer must be rounded to only have one decimal place. • 74.601  74.6

  15. Multiplying/Dividing with SigFigs • When multiplying or dividing: • The answer must have the same number of significant figures as the measurement with the fewest number of significant figures. • (22.3) (0.58) (1.114) =

  16. Multiplying/Dividing with SigFigs • (22.3) (0.58) (1.114) = • = 14.408476 • 0.58 only has two significant figures, so our answer must be rounded to two significant figures. • 14.408476  14

  17. Exact Numbers • Numbers that are known to be exact (i.e., are known for 100% certainty) do not affect the number of sigfigs in a calculation

  18. Exact Numbers • Example: • You know the density of aluminum is exactly 2.7 g/mL. You measure the mass of a sample of aluminum as 3.45 g and want to calculate the volume • D = m/v 2.7 = 3.45/v v=3.45/2.7 = 1.28 mL • 2.7 has two exact digits and 3.45 has three sigfigs. Even though 2.7 only has two, because it is an exact number, you can ignore it and round your final answer to three places (because 3.45 has three sigifgs)

  19. Exact Numbers • Example: • Batting average is calculated by dividing the # of hits a baseball player gets by the number of at-bats he has. • Because one could count exactly how many hits and at-bats a player has, no rounding is necessary – every decimal place is known for certainty!! • BA = # of hits/# of at-bats • A. McCutchen gets 200 hits in 643 at-bats, so: • 200/643 = 0.31104199... • No need to round at all because all numbers known for 100% certainty!

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