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Accuracy, Precision, And Significant Figures

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Mr. Chapman

Chemistry 20

Accuracy, Precision, And Significant Figures

- 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.

- 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.

- 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.

- 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.

- 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!

- 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"

We Will Learn These Rules, or Die Trying...

- 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.

- 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.

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.

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.

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:

- 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

- 1
- 2
- 3
- 4
- 1
- 5
- 6
- 1
- 4
- 5

- 3
- 3
- 4
- 2
- 5
- 3
- 2
- 8
- 3
- 3

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.

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)

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.

Conversion factors are considered to have an INFINITE number of significant figures