Significant Figures

1
Significant Figures

• A Reflection of Accuracy

2
Accuracy and precision

• Measurements in science should be made with
  accuracy and precision
• Accuracy being close to the actual value
• Precision measurements should be consistent

3
A graphic example
4
How to take measurements

• When measuring you can estimate the last digit
• So when using a meter stick
• The smallest mark is a millimeter
• You can estimate to the tenth of a millimeter
• Your measurement should be 14.45 cm

5
Another example

• When reading a graduated cylinder you read from
  the bottom of the meniscus
• What is the accurate and precise reading for this
  volume?

6
Significant Figures

• They reflect the accuracy of the measurements
• Includes all digits that are known to be precise
  plus one last digit that is estimated.

7
Rules for Determining Significant Figures (Know
all of these)

• All non-zero digits are significant
• Zeros to the left of non-zero digits are never
  significant
• Zeros between non-zero digits are significant
• Zeros to the right of non-zero digits are
  significant only if decimal point is shown

8
How Many Significant Figures

• 234
• 234.0
• 23400
• 23400.0
• 2304
• .00234
• 2.345
• .005
• .00405

• 3
• 4
• 3
• 6
• 4
• 3
• 4
• 1
• 3

9
Special Cases

• There are two instances where measurements have
  unlimited significant figures
• Exactly defined quanties
• 60 minutes 1 hour
• Conversion factors
• Counting exact number
• Example if you are counting 20 people in a room,
  then that number has unlimited significant
  figures.

10
Why is this of any importance

• Your answer in when doing calculations can only
  be as accurate as your least accurate measurement
• For example
• If you measure a stick as 7.9 cm. How many how
  many inches is that ? 1 inch 2.54 cm
• 7.9 cm x 1 inch/2.54 cm 3.11023622
• This answer implies accuracy beyond normal
  laboratory equipment
• Round to the least significant figures.
• 7.9 has 2 sig figs so the answer is 3.1 inches