Significant Figures: Precision and Accuracy in Measurement Darts_in_a_dartboard.jpgDarts in a dartboardPublic.

Significant Figures: Precision and Accuracy in

Measurement

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Target Practice

You have 5 arrows. Mime shooting the bow. Be sure to make a

“thwack” sound each time you shoot. Good luck!

Simple Bow

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Was the shooter accurate?Was the shooter precise?

Why or why not?

Compound Bow

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Was the shooter accurate?Was the shooter precise?

Why or why not?

Cross Bow

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Was the shooter accurate?Was the shooter precise?

Why or why not?

Which is Accurate?

Which is Precise?

Which are neither accurate nor precise?

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So, what do precision and accuracy mean in your labs? •Precision is how close your lab

measurements are to each other

•Accuracy is how close your measurements are to the correct value.

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How do we express accuracy in measurement?

• We record the measurement according to the accuracy of the equipment used plus one estimated digit.

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Remember: Estimate one digit between the lines.

What is the correct reading for the cylinder?

Meniscus

Answer:100. mL

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Read the bottom of the meniscus.

Least accurate

Mostaccurate

665 mL

20.00 mL

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Read the graduated cylinders correctly.Which cylinder is the

Which cylinder is the

Which balance is more accurate?

Estimated digit

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Rules for Significant Figures

Rule 1: Nonzeros are always signficant.

Examples:4.56

23

11,526

3 SF2 SF

5 SF

Zeros are the problem!!

• There are 3 kinds of zeros:

–CAPTURED: in the middle

–PRECEDING: on the left

–TRAILING: on the right

Rule 2: CAPTURED zeros are ALWAYS

significant.Examples:

101

200,205

7802

3 SF6 SF

4 SF

Rule 3: PRECEDING zeros are NEVER

significant.Examples:

0.00101

0.200205

0.00007802

3 SF6 SF

4 SF

Rule 4: TRAILING zeros are significant WITH A

DECIMAL present.

Examples:100

100.

0.5000

105.75060

1 SF3 SF

4 SF

8 SF

Challenge: Write one hundred in 2 SF.

Significant Figures in Calculations

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Multiplying and Dividing

• Rule 5: When multiplying or dividing the answer will have the same SF as the least accurate measurement.

Example:m = 9.567 gV = 10.1 mLD = m/V = 9.567g/10.1 mL = =

0.9472277228 g/mL0.947 g/mL

Note the use of Given, Formula, Substitute, Solve

3 SF

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Rule 6: Counted, known, and accepted values DO NOT affect

significant figures.

Example:

(20 students)(68.18 kg avg. mass) = 1363.6 kg

Round answer to 4 sig figs.

= 1364 Kg

Least accurate measurementCounted value has no affect

Adding and Subtracting

• Rule 7: When adding and subtracting, the answer is rounded to most accurate decimal place shared by all the measurements.

Example: 209.7 cm

8.004 cm

+ 1012.39 cm

1230.094 cm

Tenths column is the most accurate decimal place shared by all the measurements, so round to tenths.

Final answer: 1230.1 cm

…for now…

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