Lecture 1.2 –Units of Measurement, Sig Figs, and Uncertainty.

Lecture 1.2 –Units of Measurement, Sig Figs,

and Uncertainty

Every Chef Needs Proper Tools

• Just like chefs do in the kitchen, chemists use tools to take exact measurements of substances.

• Sometimes cooking can be an art, but chemistry is a science.

• We want to be precise and accurate.

Precision and Accuracy

• Precision – Measures how close individual measurements agree with one anothero A standard deviation (3.02 +/-

0.01) tells someone how precise you were during a laboratory.

• Accuracy – How close individual measurements agree with the “true” value.

If numbers are precise (3.05, 3.04, 3.04) does that mean they are always accurate?

When writing lab reports, include terms like precision and accuracy in your Analysis!

Exact Numbers versus Inexact #’s

• Numbers when MEASURING are inexact or exact #s.• There is always uncertainty in the last digit reported

for a MEASURED quantity; measured quantities are inexact

• Numbers that are exact for example 12 in a dozen will always be 12, it’s exact. Ignore exact #s when rounding

Quickwrite• What do you think is the difference

between 4.0 grams and 4.000 grams?

4.0 g implies that 4.0 has more uncertainty and that the true value is closer to 4.0 than it is to 3.9 or 4.1

4.000 has less uncertainty meaning that the true value is closer to 4.000 than it is to 3.999 or 4.001

More accurate!

Significant Figures• Sig Figs are of critical importance in the lab. • They indicate the accuracy of a

measurement or a calculation. • We don’t want errors based on random ways for

rounding or random ways of presenting an answer.

The AP FRQ’s will require answers reported to the CORRECT amount of sig figs.

1 mL may be considered wrong, but 1.0mL may be considered right!

Determining the Number of Sig Figs

• The most important rule is that all nonzero digits in any measurement are significant:

1. Zeros between nonzero digits are always significant. For example, 1005 has ______ sig figs.

2. Zeros at the beginning of a number are never significant. For example, 0.005 has _____ sig fig.

3. Zeros at the end of a number are significant only if there is a decimal. For example, 3.0 has ____ sig figs, but 30 has _______ sig fig.

4

2

1

1

What about #’s in Scientific Notation?

• Recall that we can write a number like 10,300 in scientific notation as 1.03 x 104

• This number would have _____ sig figs3

Scientific Notation• 10000 = 1 x 104

• 24327 = 2.4327 x 104

• 1000 = 1 x 103

• 100 = 1 x 102

• 482 = 4.82 x 102

• 10 = 1 x 101

• 89 = 8.9 x 101

• 1 = 100

• 1/10 = 0.1 = 1 x 10-1

• 0.053 = 5.3 x 10-2

• 1/1000 = 0.001 = 1 x 10-3

• 0.0078 = 7.8 x 10-3

• 1/10000 = 0.0001 = 1 x 10-4

• 0.00044 = 4.4 x 10-4

Rules: 1. A number other than zero must

be at the front followed by a decimal.

2. x10 tell you the number of times you moved the decimal to achieve rule #1

3. If the original number is bigger than 1 then the exponent is positive

4. If the original number is smaller than 1 (decimal) then the exponent is negative.

1.6 x 10-

19 C

Sig Figs for Calculations

Determine sig figs only after a calculation is complete.

Sig Fig for Addition/Subtraction

• When you add/subtract numbers, the answer has the same number of decimal places as the number with the least decimal places.

Round off to one decimal place since 83.1 has the least number of decimal

places!Final answer you report is 104.8

Another example• Three measurements were recorded (inexact or

exact number?) below: 0.039 g, 0.4 g, 0.09 grams.

A) Accurately show the sum of those measurements.

B) Are the three numbers precise? Why or why not?

Another example• Three measurements were recorded (inexact or exact

number?) below: 0.039 g, 0.4 g, 0.09 grams.

A) Accurately show the sum of those measurements. 0.529 = 0.5g (least decimal place!)

B) Are the three numbers precise? Why or why not?

Another example• Three measurements were recorded (inexact or

exact number?) below: 0.039 g, 0.4 g, 0.09 grams.

A) Accurately show the sum of those measurements.

B) Are the three numbers precise? Why or why not? None of the 3 are precise to one another. The numbers are not close to one another.

Sig Figs for Multiplication/Division• When you multiply or divide numbers, the answer

has the same number of sig figs as the number with the fewest sig figs.

4 sig figs

2 sig figs, so the answer needs 2 sig

figs 32 cm2

Another Example• Find the volume of a cylinder whose radius is 5

meters and its height is 1.0 meters. Volume of a

cylinder is V = πr2 h

Another Example• Find the volume of a cylinder whose radius is 5

meters and its height is 1.0 meters. Volume of a cylinder is V = πr2

• V = π(5m)2(1.0m) = 78.5m3 (how would you turn this into one sig fig?)

• 8 x 101 m3 convert into scientific notation

• 80 accepted too. (1 sig fig)

What if you have both?Step 1: Use PEMDAS. Step 2: You either multiply/divide or add/subtractStep 3: At the end of each step, you must ask yourself,

What is the next operation that I will perform on the number that I just calculated?

• If the next operation is in the same group of operations that you just used (example: multiply/divide) then do NOT round yet

• If the next operation is from the other group (add/subtract), then you must round off that number before moving on to the next operation.

Example:Compute: [(3.5 x 3.333)] / [(3.04 x 3.0)]

• Since it’s all multiply/divide, don’t round until the very end! The lowest sig fig is two, so your answer must be rounded to one sig fig

• 1.279 (did you get this?) • Now round to 2 sig figs: 1.3

Example 2:Compute: [(3.5 + 3.333)] / [(3.04 - 3.0)]

1 dec place 1 dec place• Do what’s in parenthesis first (PEMDAS) and

immediately round to appropriate sig figs since you’ll be dividing soon! (see rules)

[6.8/0.04] =[6.8/4.0x10-2]= 170 = 1.7 x 102 1 sig fig 2 sig figs

SI Units: Metric System

• The metric system is based on the power of 10. • These powers of 10 will convert you back to the base unit.

Once you are at the base, you can convert to the desired unit. This makes no sense to me! It will later…

• First, know these 6 Base Units

oGrams is for mass oMeters for length oSeconds for time oKelvin for temperature oMoles for amount of substance oAmpere for current

Base units don’t have prefixes!!!

Water Measurements • Temperature measures how cold or hot some

object is. In chemistry, we use Kelvin as units. o 0 Kelvin is the lowest temperature that exist (absolute

zero)

Know this about Water• The freezing point of water is 00C. • The boiling point of water is 1000C• Density is in mass/volume • Density of water is 1g/cm3 or 1g/mL

Memorize these

prefixes and conversion!

Prefix Factor

Milli- (m) 10-3

Centi- (c) 10-2

Deci- (d) 10-1

Base 100

Deka- (D) 101

Hecto- (H) 102

Kilo- (k) 103

Ends in –i you know it’s small

Ends in –a or –o you know it’s big

How to read this: (a lot of the small stuff!)• 1 kg (big) = 1,000 grams • 1 m = 100 cm (small)• 1 L = 1000 mL (small)• 109 nanometers (small) = 1 meter

This is one way you can remember what equals what.

The second way is to use base units

• Base units don’t have prefixes. • Whatever the meaning of a prefix is, you put that

directly next to the base! That’s why it’s called a base, you put it on the base!

If I ask you to convert 1 m into cm (base is meters) (centi means 10-2)

10-2 meters are in 1 cm OR 1m = 100 cm same thing

Sig. Fig Practice• Complete Problem Set 1.2• Be sure to use the appropriate units!