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Accuracy, Precision, And Significant Figures

Mr. Chapman Chemistry 20. Accuracy, Precision, And Significant Figures. Accuracy and Precision. It is important to note that accuracy and precision are NOT the same thing. Data can be very accurate, but not precise. Data can be very precise, but not accurate.

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Accuracy, Precision, And Significant Figures

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  1. Mr. Chapman Chemistry 20 Accuracy, Precision, And Significant Figures

  2. Accuracy and Precision • It is important to note that accuracy and precision are NOT the same thing. • Data can be very accurate, but not precise. • Data can be very precise, but not accurate. • These sound like weird statements, but we’ll explain them here.

  3. Accuracy • Accuracy refers to how close a measured value (such as one that you get in a lab experiment) is to an actual value (the one generally excepted by people). • For example, if I was measuring a room that was said to be 24 feet wide, and I measured that it was 23.9 feet wide, I would be very accurate.

  4. Precision • Precision refers to how reproducible your result is. • Imagine I do an experiment 3 times to measure volume, and that these are my measurements: 2.9 mL, 3.1 mL, 3.0 mL • Those are precise measurements, because they are all close in value.

  5. Precision Continued... • Now imagine I do the same test, but this time I get these values: 3.0 mL, 5.9 mL, 1.0 mL. • These values all average out to about 3.0 mL, but they are not precise at all. • Accuracy vs. precision is an important distinction to make, and the graphic in the next slide helps with it.

  6. Accuracy vs. Precision

  7. Degrees of Accuracy • In chemistry, any instrument that we use can only be so accurate. This accuracy is always limited to the gradations of the instrument. • For example, you wouldn’t use a metre stick to measure the width of a bacterial cell, would you? It doesn’t measure that low!

  8. Degrees of Accuracy: • As a general rule, the degree of accuracy is half a unit on each side of the measure. The picture will make sense: If your instrument measures in "1"s then any value between 6.5 and 7.4 is measured as "7" If your instrument measures in "2"s then any value between 7 and 9 is measured as "8"

  9. We Will Learn These Rules, or Die Trying... Significant Figures

  10. Significant Figures • Most people ask why we need to worry about significant figures. • The fact is, in science you can never report a number to be more certain than you know it to be. • For example, if I use a meter stick, I can never tell you that something is 1.23456 m long, because I am not that certain.

  11. Significant Figures • Because of this, we always need to report our numbers in the number of figures that we are sure of. In other words, the figures that are significant. • There are many rules for significant figures, but they are not hard if you commit to learning them and practice.

  12. Rules for Significant Figures • All digits 1 – 9 inclusive are significant. Ex: The number 2134 has 4 significant figures. • Zeros placed between significant figures are always significant. Ex: The number 2004 has 4 significant figures.

  13. Rules for Significant Figures • Zeros placed before other digits are not significant – they are placeholders. Ex: The number 0.046 has 2 significant figures. • Zeros placed after other digits are not significant, they are also placeholders. Ex: The number 5000 has only 1 significant figure.

  14. Rules for Significant Figures • Zeros placed after other digits but behind a decimal point are significant. Ex: The number 7.9100 has 5 significant figures. Try these examples, young chemists:

  15. Identify the Number of Sig. Figs: • 0.02 • 0.020 • 501 • 501.0 • 5000 • 5000.0 • 6051.00 • 0.0005 • 0.1020 • 10001 • 8040 • 0.0300 • 699.5 • 2.00 x 102 • 0.90100 • 90100 • 4.7 x 10-8 • 108000.00 • 3.01 x 1021 • 0.000410

  16. Identify the Number of Sig. Figs: • 1 • 2 • 3 • 4 • 1 • 5 • 6 • 1 • 4 • 5 • 3 • 3 • 4 • 2 • 5 • 3 • 2 • 8 • 3 • 3

  17. Rules For Calculations With Significant Figures • When we do arithmetic, we need to be careful with the number of significant figures that we use. • You can also be as sure about a number as your least certain measurement. This is the guiding principle in these rules.

  18. Rules For Calculations With Significant Figures • When you multiply and divide, limit and round your answer to the least number of significant figures present in the mathematical operation. • Example: 23.0 cm x 432 cm x 19 cm = 188,784 cm3 which we round to 190,000 cm3 (2 significant rigures)

  19. Rules For Calculations With Significant Figures • When you add and subtract, limit and round your answer to the least number of decimal places in any of the numbers present in the mathematical operation. • Example: 123.35 mL + 46.0 mL + 86.257 mL = 255.607 mL which we round to 255.6 mL.

  20. One Last Point... Conversion factors are considered to have an INFINITE number of significant figures

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