Measured & counted numbers• When you use a measuring tool to

determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.

Counted numbersObtained when you count objects• 2 soccer balls• 1 watch• 4 pizzasObtained from a defined relationship• 1 foot = 12 inches• 1 meters = 100 cm

Not obtained with measuring tools

Measurements:Accurate or Precise?

Creating definitions and clarifying terms

Precision• Precision is the ability to _______________and

come up with the same value every time.• It is an indication of __________a series of

measurements are to each other.• In general, the more decimal places you have,

the more precise your measurement is.

Precision• The idea of precision is very closely aligned

with the idea of significant figures.• A large number of significant figures

suggests a high degree of precision.• In our next class we will learn all about sig

figs. Now, relax

Which is the most precise balance?

Accuracy• An indication of how

________________________ (often theoretical)

The closer you are to the real, accepted value, the more accurate you are.

Accurate or Precise?Case 1

• In the diagram, what can we say about the group of arrows in terms of

accuracy:

precision:

Accurate or Precise?Case 1

• In the diagram, what can we say about the group of arrows in terms of

accuracy:low (as a group)

precision:low

Accurate or Precise?Case 2

• In the diagram, what can we say about the group of arrows in terms of

accuracy:

precision:

Accurate or Precise?Case 2

• In the diagram, what can we say about the group of arrows in terms of

accuracy:low

precision:high

Accurate or Precise?Case 3

• In the diagram, what can we say about the group of arrows in terms of

accuracy:

precision:

Accurate or Precise?Case 3

• In the diagram, what can we say about the group of arrows in terms of

accuracy:high

precision:high

Can we ever be 100% certain??Nope!This is what we call ‘uncertainty’ in measurements.

Experimental uncertainty

• It is the estimated amount by which a measurement might be in error

• Usually expressed as +/-• The smaller the uncertainty, the more the

precision…

Experimental uncertainty

Assume you measured a temperature to be 37.5 C°What would the uncertainty be?Uncertainty is always in the last digit!What does this mean?

Experimental uncertainty

This means, the actual degree is somewherebetween

How to read a measurement scale

Taking measurements

Example b) page 31

Volume readings

Graduated cylinder readings

Time to practice!

Hebden page29 #44 page32 #48(A,C,E) page34 #50(A,D,G) page35 #51(A,C) and #52(A,B)

I am here to help

Measurements • Why do we care??????

• Measured quantities have uncertainties in them. It is impossible to find the EXACT value…so what do we use?

Significant figures• They are measured or meaningful digits.How do we know if a number is a ‘sig fig’ or

not? • Let us proceed, shall we?

Two major cases to know

#1: When there are no decimal points

#2: When there are decimal points

#1: when there are no decimal points

• Count every single number you see as a significant figure, EXCEPT for ZERO.

• BUT…..Zeroes in between two non-zero digits are significant. All other zeroes are insignificant.

#1: when there are no decimal points

• How many sig figs do the following numbers have??

345, 5557, 300, 4120, 4005, 40050

#2: when there are decimal points

• Start from the left side of the number, ignore all the zero's on the left side of the decimal points ( aka leading zero's). Only start counting at the first non zero digit. Once you start counting, continue until you run out of digits.

#2: when there are decimal points

• Example: how many sig figs do the following numbers have?

32.670, 0.0001, 0.034780, 44.4, 00.9090

Significant figures

“sig figs”

0.5200.00255000.02300120035500.2.0 x 105

3214632 do not expand

Significant figures

“sig figs”2.50020.0065050010.02003000.02010200200.2.0 x 102

2. x 102

534641321

Adding and Subtraction with Significant Figures

When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations. 1.

21.036 + 22.1

Adding and Subtraction with Significant Figures

When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations

3.301.2256

- 0.36

Adding and Subtraction with Significant Figures

4. 8.053 x 104

+ 2.3 x 104

Adding and Subtraction with Significant Figures

5.2.463 x 105

+ 5.006 x 102

Adding and Subtraction with Significant Figures

6. 5.331 x 10-4

- 2.126 x 10-5

When changing exponents, remember…..if you change the lower exponent to the higher exponent. You are making the exponent larger so make the number smaller. It is a trade !

HOMEWORK• PAGE 40 #57 (A,B,C,E,F,I,J)