do now: (3 minutes) 1. what are the definitions of precision and accuracy? 2. why are precision and...

Do Now: (3 minutes)Do Now: (3 minutes)1. What are the definitions of precision

and accuracy?2. Why are precision and accuracy

important when making measurements?

Do Now Discussion:Do Now Discussion:

Precision: how close a set of measurements are to each other

Accuracy: How close an experimental value is to the actual value

We need to be accurate in order for our results to be valuable and we need to be precise in order for our results to be valid.

Significant Figures and Significant Figures and RoundingRounding(sig figs)(sig figs)

CORNELL NOTESCORNELL NOTES9/28/099/28/09

SIGNIFICANT FIGURESSIGNIFICANT FIGURES

The reliable digits in a measurement based on the accuracy of the measuring tool.

The number of digits we use when recording a measurement

GENERAL INFO ON SIG FIGSGENERAL INFO ON SIG FIGS

Sig figs give you information on the EXACTNESS of a measurement

When measuring, ONLY ONE estimated digit is allowed to be significantExamples:

Meter stickGraduated cylinder

RULE #1: RULE #1: Nonzero Nonzero digits are always digits are always significantsignificant

324455 sig figs

0.234355 sig figs

2348.236 sig figs

Quick Check:Quick Check:

Hold up the number of fingers representing the number of significant figures

How many significant figures are in the number 3.127?

FOUR!

RULE #2: RULE #2: Zeros are weird Zeros are weird and come in 3 typesand come in 3 types

TYPE 1: Leading Zeros

TYPE 2: Captive Zeros

TYPE 3: Trailing Zeros

RULE #2.1 (Leading RULE #2.1 (Leading Zeros):Zeros): These come before non-zero digits These come before non-zero digits and don’t count. and don’t count. They are only They are only placeholders.placeholders.

0.00232 sig figs

0.023004 sig figs

RULE #2.2 (Captive RULE #2.2 (Captive Zeros):Zeros): These are between nonzero digits. These are between nonzero digits. They always count as sig figs.They always count as sig figs.

1.0094 sig figs

230,0046 sig figs

RULE #2.3 (Trailing RULE #2.3 (Trailing Zeros):Zeros): Zeros at the right end of the Zeros at the right end of the number. They are significant only number. They are significant only if the numbers has a decimal if the numbers has a decimal point.point.100 = 1 sig fig

1.00 = 3 sig figs100. = 3 sig figs

Quick Check:Quick Check:

Hold up the number of fingers representing the number of significant figures in the following:

1.How many sig figs in 0.00234?THREE!

1.How many sig figs in 230?TWO!

RULE #3: EXACT RULE #3: EXACT NUMBERSNUMBERS

Exact numbers have an infinite number of significant figures.

◦Non-measured numbers (things we count, 8 atoms)

◦Formulas/equations (area = πr2)

◦Definitions (1m = 100 cm)

MathematicaMathematical Operations l Operations and and SigFigs SigFigs

Addition & Addition & SubtractionSubtractionThe answer must have

as many decimal places as the

measurement having the least number of

decimal places.

12.11

18.0

1.013

31.123 = 31.1

12.11005

0.0004

1.0

11.10965 = 11.1

Addition Subtraction

Quick Check:Quick Check:

Hold up the number of fingers corresponding to the number of sig figs in the following:

15.67 + 14.3 = 29.97THREE!

29.97 ≈ 30.0

Multiplication & Multiplication & DivisionDivision

The answer may contain only as many significant

digits as the measurement with the

least number of significant digits

4.56 1.4 = 6.38 Corrected 6.4

10 19.031.903 2

Multiplication

Division

2 sigfigs3 sigfigs 2 sigfigs

1 sigfig4 sigfigs 1 sigfig

Quick Check:Quick Check:

Hold up the number of fingers corresponding to the number of sig figs in the following:

6.0 x 8.97 = 53.82TWO!

53.87 ≈ 54

Rules for RoundingRules for RoundingRule 1: If the digit to be removed is less than 5,

the preceding digit stays the same; if it is equal to or greater than 5, round the preceding digit up.

3.04999 = 3.03.05999 = 3.1

Rule 2: In a series of calculations, carry the extra digits through to the final result, THEN round

3.05 x 5.555 x 3.0 = 50.82825 = 51NOT

3.1 x 5.6 x 3.0 = 52.08 = 52

Quick Check:Quick Check:

In the following question, use your fingers to represent what the digit will be rounded to. (i.e. if it’s rounded up to 2, hold up 2 fingers)

When the 4.5237 is rounded to the first decimal point, what is the answer?

4.5!

Deal of the Week:Deal of the Week:Every day we will have a “challenge”

set of questions to answer in partners

If 100% of the students present participate

If at least 80% of the class answers ALL questions correctly…

NO QUIZ ON FRIDAY!You have 30 seconds to find and sit with a partner!

Challenge Questions:Challenge Questions:On the small sheet of paper, write your name

and your partner’s name, the date and the period. Then answer the following questions on that paper:

1.How many significant figures are in 1.23097?

2.How many sig figs are in 5000?3.What is 2.34 + 5.2?4.What is 8.97 x 7.124?5.Why are significant figures important?

Homework ProblemsHomework Problems

Due on Friday!Percent Error:

◦ p.49 # 32, 33, 34Significant Figures:

◦ p. 51 # 35abd, 36abd◦ p. 53 # 38, 40

Density: ◦ p. 38 # 1, 3

Dimensional Analysis: ◦ p. 45 # 19