Unit 1: Basics // Metrics & MatterEssential Question: How do scientists express the degree of uncertainty in their measurements?

Thursday, September 11, 2014

Because nothing in science is ever certain…

Do Now

•Use the ruler you have been given to measure the short side of the bill to the best of your ability

•Record your measurement in the given section in your notes

Quantitative Observation

=measurements; must consist of two parts: a number and a unit

Ms. Ngo is 5’2”

What would happen if we did not have units??

Ms. Ngo is 52

Uncertainty

•Any measurement involves an estimate and thus is uncertain to some extent

Person Measurement1 2.85 cm2 2.84 cm3 2.86 cm4 2.85 cm5 2.86 cm

If 5 different people took a measurement of a pin, we could have 5 different measurements:

We saw this during the Do Now activity!

Person Measurement1 2.85 cm2 2.84 cm3 2.86 cm4 2.85 cm5 2.86 cm

If 5 different people took a measurement of a pin, we could have 5 different measurements:

The first two digits are the same regardless of who made the measurement (these are

called certain numbers))

Person Measurement1 2.85 cm2 2.84 cm3 2.86 cm4 2.85 cm5 2.86 cm

If 5 different people took a measurement of a pin, we could have 5 different measurements:

The last digit varies; it is called the uncertain number

Accuracy•Measure of how close a

measurement comes to the actual/accepted value

•Accepted Value = 24 cm

•Measured Values(Experimental Values)

Measurements

24.1 cm

24.0 cm

23.9 cm

Precision

•Measure of how close a series of measurements are to one another

Measurements

88.7 in

88.8 in

88.9 in

88.7 in

Group Discussion

* *The more numbers the more precise the tool

Series of Measurements Can Be…

Think-Pair-Share…

• Six students used this ruler to measure the metal strip shown. Their measurements are listed in the table.

• In terms of accuracy and precision, how would you classify their measurements?

Review

•Compare the precision of a 100 mL graduated cylinder with 1 mL increments with a 50 mL graduated cylinder with 0.5 mL increments.

▫A 50 mL graduated cylinder with 0.5 mL increments is more precise because the increments are smaller

Review• The chart below shows the volume of a solution

measured by four different groups. The actual (correct) volume of the solution is 44.5 mL.

▫What group has both accurate and precise data? Group 1

▫What group has data that is imprecise and inaccurate? Group 2

▫Comment on the accuracy and precision of Group 3’s data? Their data is precise and inaccurate.

Volume (mL) Group 1 Group 2 Group 3

Trial 1 44.5 mL 42.3 mL 49.0 mLTrial 2 44.6 mL 47.2 mL 49.1 mLTrial 3 44.5 mL 48.0 mL 49.0 mL

Review

•To determine the length of a running shoe, a cross-country runner measured the shoe several times using a metric ruler. If the true length of the shoe is 88.74cm, give an example of:▫imprecise and inaccurate data ▫precise but inaccurate data ▫precise and accurate data

Measuring Volume in the Lab

•Volume is measured from the bottom of the meniscus

•Take the Volume!

(Always take a measurement to the first uncertain number.)

•Correct Answer:

56.0 mL

•Take the Volume!

(Always take a measurement to the first uncertain number.)

•To be correct, your answer must be in the following range:

8.40-8.49mL

Percent Error

•Used to gage how close an measurement taken via experiment is to the accepted value

% Error =|Experimental-Accepted|

Accepted Value

Do not have to memorize formula; It’s located on last page of Reference Table

22

Significant Figures in MeasurementThe numbers reported in a measurement are limited by the measuring tool

Significant figures in a measurement include the known digits plus one estimated digit

23

Counting Significant Figures

Number of Significant Figures

38.15 cm 45.6 ft 265.6 lb ___122.55 m ___

Complete this sentence: All non-zero digits in a measured number are

(significant or not significant).

5

3

24

Leading Zeros

Number of Significant Figures

0.008 mm 1

0.0156 oz 3

0.0042 lb ____

0.000262 mL ____

Complete this sentence : Leading zeros in

decimal numbers are

(significant or not significant).

3

2

25

Sandwiched Zeros

Number of Significant Figures

50.8 mm 3

2001 min 4

0.702 lb ____

0.00405 m ____

Complete: Zeros between nonzero numbers are (significant or not significant).

3

3

26

Trailing Zeros

Number of Significant

Figures

25,000 in. 2

200 yr 1

48,600 gal 3

25,005,000 g ____ Complete: Trailing zeros in numbers without decimals are

(significant or not significant) if they are serving as place holders.

5

27

Learning Check

In which set(s) do both numbers contain the same number of significant figures?

1) 22.0 and 22.00

2) 400.0 and 40

3) 0.000015 and 150,000

28

Learning Check

State the number of significant figures in each of the following:

A. 0.030 m 1 2 3

B. 4.050 L 2 3 4

C. 0.0008 g 1 2 4

D. 3.00 m 1 2 3

E. 2,080,000 bees 3 5 7

29

Learning Check

A. Which answers contain 3 significant figures?1) 0.4760 2) 0.00476 3) 4760

B. All the zeros are significant in 1) 2.050 x 103 2) 25.300 3) 0.00307

C. 534,675 rounded to 3 significant figures is

1) 535 2) 535,000 3) 5.35 x 105

4 33

30

Independent Practice

•Worksheet

•Work alone or with a partner

•Perfect time for questions

Significant Figures in Calculations & RoundingUnit 1: Measurement & Matter

1. COMPUTE answer first!!!!

2. CHOOSE whether to round based on sig figs or decimal places

Rounding w/ Sig Figs

CALCULATION RULES

• For Multiplication & Division

limiting term = one w/ the SMALLEST # of sig figs

CALCULATION RULES

• Multiplication & Division

Round answer to the same number of sig figs as the answer with the fewest sig figs

Example

4.56 x 1.4 = Round to 6.4 3 sig

figs2 sig figs

2 sig figs

6.384

Example

1.234 x 3 = Round to 4 4 sig figs

1 sig fig

1 sig fig

3.702

• For Addition & Subtraction

limiting term = one w/ the smallest number of DECIMAL PLACES

CALCULATION RULES

• Addition & Subtraction

Round answer to the same number of decimal places as the measurement with the fewest decimal places

CALCULATION RULES

12.161 + 3.12 =

Significant Figures in Calculations

Round to 15.283 decimal

places2 decimal

places 2 decimal places

15.281

6.8 + 3 =

Significant Figures in Calculations

Round to 101 decimal

place0 decimal

places 0 decimal places

9.8

41

Summary•Only as precise as your “weakest link”

▫The one w/ fewest sigs figs/decimal places

▫Multiplication/ Division-> sigs figs▫Addition/Subtraction -> decimal places

1. 2.45 x 3.5

2. 8.315 ÷ 298

3. 135 x 246 x 0.000556 x 0.0998 x 155

4. 3.6x10-3 x 8.123

You Try….

8.6

0.0279286

0.029 or 2.9x10-2

5. 12.11 + 18.0 + 1.013 =

6. 29.63 + 24.798 + 1.263 =

7. 1081 – 7.25 =

8. 8.445 x 105 – 9.44 x 102 =

You Try…

31.1

55.691074

8.44 x 105