Warm-up:

• Are cell phones and ipods allowed in the classroom? • What will happen to them if the

teacher sees or hears one (that includes headphones)?

Significant Figures - Measurements

• NO measurement is perfect. – All measurements have an uncertainty.– Human error IS NOT the cause of the uncertainly.

• Read and record a measurement to one decimal place beyond the smallest marking on that piece of equipment.

• With a digital device, record all digits.

What is the Length?

• We can see the markings between 1.6-1.7cm• We can’t see the markings between the .6-.7• We must guess between .6 & .7• We record 1.67 cm as our measurement• The last digit an 7 was our guess...stop there

3

1 2 3 4 cm

0 1 2

0 1 2

0 1 2 3 4 5

0 1 2

0 1 2 3 4 5

0 1 2

Warm-up :

• Determine which of the following would give a more precise number if used.

– OR

0 10 1

Where do we measure liquids

ABC

Always measureliquids at thebottom of the meniscusAND at eye level

5

4

3

2

1

0

2

1

0

5

4

3

2

1

0

1

0

Warm-up:

• Measure the following using proper measuring technique so the answer has the correct number of sig figs.

0 1 20 1 2 3 4 5

Accuracy

• Agreement with accepted or true value.• “Correctness”

Precision

• The degree to which a set of data agrees with each other.

• A smaller range, the more precise the data.

19. Which one is accurate but NOT precise

A B

DC

20. Which one is precise but NOT accurate

A B

DC

21. Which one is NOT accurate and NOT precise

A B

DC

22. Which one is accurate AND precise

A B

DC

Accuracy and Precision

Accuracy and Precision in Measurements

Reading Thermometer 1

Thermometer 2

Thermometer 3

Thermometer 4

1 99.9°C 97.5°C 98.3°C 97.5°C

2 100.1°C 102.3°C 98.5°C 99.7°C

3 100.0°C 99.7°C 98.4°C 96.2°C

4 99.9°C 100.9°C 98.7°C 94.4°C

Average 99.98°C 100.1°C 98.5°C 96.9°C

Range 0.2°C 5.0°C 0.4°C 5.3°C

Accurate

Precise

YES

YES

YES

YES

NO NO

NONO

To number or not to number, that is the question…..

• Observations or data that deals with numbers is called QUANTITATIVE.

• Observations or data that does NOT deal with numbers is called QUALITATIVE.

Qualitative or Quantitative?

1. There are 6 tables in the room– A) Qualitative – B) Quantitative

2. The room is hot– A) Qualitative – B) Quantitative

3. This powerpoint sucks– A) Qualitative – B) Quantitative

4. There are lot of people in this room– A) Qualitative – B) Quantitative

Types of Quantitative Information

• There are 2 types of quantitative data– Exact• Anything that is counted

– Ex. I have 10 fingers and 10 toes

• Exact relationships or predefined values– 12 inches = 1 foot– 1 dozen = 12

– Inexact (measured)• Anything that you measure using a tool (ruler, scale,

thermometer, etc)– The paper is 8.5 inches wide

Exact or Inexact #’s

5. 1 yard = 3 feet– A) Exact– B) Inexact (measured)

6. The diameter of a red blood cell is 6 x 10-4cm.– A) Exact– B) Inexact (measured)

7. There are 2 doors in this room.– A) Exact– B) Inexact (measured)

8. Gold melts at 1064°C– A) Exact– B) Inexact (measured)

Warm-up

• Come up with an example of the following:• Exact number• Inexact number• Quantitative observation• Qualitative observation

Significant Figures

• The significant figures (sig figs) of a number are those digits that carry meaning contributing to its precision.

• Exact numbers have an infinite number of sig figs

• Inexact numbers have a finite number based on rules of sig figs.

Significant Figures

• All non-zero numbers are always significant. Then use the following to determine if zeros are significant.–Determine if number has a decimal point.– If it does, look from left to right for the first

non-zero digit. All digits after it are significant– If it does not, go from right to left looking for

the first non-zero digit. All digits after it are significant.

Significant Figures –Zero Rules

Counting Sig Figs No decimal

254 3 SF304,900 4 SF

Counting Sig Figs with Decimal

0.00450 3 SF7 SF1,000.000

Practice: How Many Sig Figs?

0.00003280 g

1000 mL

3.14 m

21.001 cm

3 SF

5 SF

1 SF

4 SF

Sig. Figs. in Calculations Addition and Subtraction

• By doing a math operation, you can not increase the number of significant figures!

• Addition and Subtraction – count DECIMAL PLACES– The number of decimal places in your answer

should match the digit with the smallest number of decimal places.

Sig. Figs. in Calculations Multiplication and Division

• Multiplication and Division – Count SIGNIFICANT FIGURES.– The number of significant figures in your

answer should match the digit with the smallest number of significant figures.

Adding & Subtracting Sig Figs

3.224 cm + 1000.3 cm = 1003.5 cmEstimated value Estimated value

Practice

56.333 g + 1.0007 g =

25.005 L + 38.1 L =

0.01 g + 1.11 g =

3000 N + 144.2 N =

63.105 = 63.1 L

57.3337= 57.334 g

1.12

3144.2

g

= 3144 N

1.12

Multiplying & Dividing Sig Figs

6.0 cm X 22.0 cm =2 SF 3 SF3 SF

132 =130 cm2

2 SF

Practice

56.3 g 33 mL =

4.0 m X 22.3 m =

0.21 cm X 1.11cm X 2.0 cm =

89.2 = 89 m2

1.7060606 = 1.7 g/mL

0.46620.47 cm3