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Quantitative vs. Qualitative

- Make a quantitative observation about your

textbook - Make a qualitative observation about your textbook

Quantitative vs. Qualitative

- Quantitative observation
- Qualitative observation

Precision vs. Accuracy

- Archery Activity

Precision vs. Accuracy

- Which is more precise for measuring volume, a

beaker or a graduated cylinder?

Precision vs. Accuracy

- Accuracy refers to the closeness of

measurements to the correct or accepted value of

the quantity measured. - Precision refers to the closeness of a set of

measurements of the same quantitiy made in the

same way.

Precision vs. Accuracy

- Measured values that are accurate are close to

the accepted value - Measured values that are precise are close to one

another but not necessarily close to the accepted

value

Darts within small area High precision

Area covered on bulls-eye High accuracy

Darts within small area High precision

Area far from bulls-eye Low accuracy

Darts within large area Low precision

Area far from bulls-eye Low accuracy

Darts within large area Low precision

Area centered around bulls-eye High accuracy

(on average)

Unit conversions

- Copy metric conversion from book

Unit Conversions

- Practice problems
- 750 km __________m?
- 283 m __________km
- 112 Mwatt __________Kwatt?
- 112 Mwatt __________Gwatt

Scientific Notation Significant Figures

Unit Estimation

Scientific Notation

- Used to make numbers more usable
- 1,000,000,000 1x109
- 0.00000000011x10-10

How do you figure this out?

- You move the decimal until you have only one

digit in front of the decimal. - If you move right, then the exponent will be

NEGATIVE based on the number of places your

decimal moved. - If you move left, then the exponent will be

POSITIVE based on the number of places your

decimal moved.

Practice

- Give the following in scientific notation
- 6,289,030,987
- 0.004500678
- 5.60987
- 568.2365400
- 35.98340002
- 0.23476

Give the following inscientific notation

- Practice
- 6,289,030,987
- 0.004500678
- 5.60987
- 568.2365400
- 35.98340002
- 0.23476

- 6.289030987x109
- 4.500678x10-3
- 5.60987
- 5.682365400x102
- 3.59834002x10
- 2.3476x10-1

Going the other way

- 1.3487x105
- 4.9800456x104
- 2.345x101
- 5.6789x10-3
- 3.591x10-1
- 2.0080x10-2

- 134,870
- 49,800.456
- 23.45
- 0.0056789
- 0.3591
- 0.020080

Try For Yourself

- 7.234x10-5?
- 8.234x103?
- 5.000x10-4?
- 9.99998x10-2?
- 8.555x106?

ANSWERS

7.234x10-5 0.000 072 34 8.234x103

8,234 5.000x10-4 0.000 500 0 9.99998x10-2

0.099 999 8 8.555x106 8,555,000

Significant Digits - What is it?

- When we take measurements in science, we can only

be sure of our numbers to a certain point - The numbers we are sure of are called significant

digits or significant figures (sig figs)

Sig Figs - How do we use them?

- Two types
- Measured
- You actually measure and record your answer to a

certain digit - Calculated
- You use already measured numbers to compute an

answer

Measured Sig Figs

- Questions you can answer
- How long is your book?
- Measure it with a meterstick and read the length.
- What is the mass of an orange?
- Put it on a scale and read the mass.
- How much milk is in the carton?
- Pour the milk into a graduated cylinder and read

the volume.

Calculated Sig Figs

- Sometimes, youve collected the data and you need

to calculate a final answer - Example - you find the length, width and height

of your book and you want to find the volume. - You need to multiply the three numbers together

to get an answer.

Determining what countsSig Fig Rules!

- All non-zero numbers are significant
- Example 1,2,3,,9
- All zeros between non-zero numbers are

significant - Example 1080.305
- All zeros before a written decimal are

significant - Example 600.

More Rules

- All zeros following non-zero numbers, after a

decimal are significant - Example 1.00 0.003470030
- These rules are to determine what counts when you

are looking at a number.

Practice

- How many sig figs are in the following numbers?
- 2.341
- 0.0004580
- 560
- 560.
- 560.0003

Answers

- 2.341 has 4 sig figs
- All the numbers are non-zero digits, so they all

count!

Answers

- 0.0004580 has 4 sig figs
- The three non-zero numbers 458 and the zero

following this set - The first four zeros are place holders - they get

the 4 into ten thousands place

Answers

- Another way to think about 0.0004580 having four

sig figs is to write it in scientific notation - 0.00045804.580x10-4
- When you write in scientific notation, you only

write the sig figs before you write the

x10whatever - So here you see that you wrote the 4, 5, 8, and

0. Those are the sig figs!

Answers

- 560 has 2 sig figs
- This one is tricky. Notice that there is no

decimal, so the zero is just a place holder to

get the 6 into the tens spot.

Answers

- 560. Has 3 sig figs.
- This time the zero counts because the decimal

means it was actually measured.

Answers

- 560.0003 has 7 sig figs
- All zeros are between non-zero digits, so they

are all significant.

How do you know when to stop?

- When youre measuring, you know when to stop

based on your equipment. - If your equipment reads to the tens, then you can

guess up to one more place. You can read to the

ones - Lets look at it.

Multi step calculations

- Keep One Extra Digit in Intermediate Answers
- When doing multi-step calculations, keep at least

one more significant digit in intermediate

results than needed in your final answer. - For instance, if a final answer requires two

significant digits, then carry at least three

significant digits in calculations. If you

round-off all your intermediate answers to only

two digits, you are discarding the information

contained in the third digit, and as a result the

second digit in your final answer might be

incorrect. (This phenomenon is known as

"round-off error.")

2 Greatest Sins in Sig Figs

- Writing more digits in an answer (intermediate or

final) than justified by the number of digits in

the data. - Rounding-off, say, to two digits in an

intermediate answer, and then writing three

digits in the final answer.

Reading the right number of digits.

- Ruler/Meterstick
- Graduated Cylinder
- Beaker
- Scale

Calculations - The rules!!!

- Addition/Subtraction
- Your answer should have the same number of

decimal places as the number with the least

number of decimal places - Multiplication/Division
- Your answer should have the same number of sig

figs as the number with the least number of sig

figs - Always follow the order of operations!

Practice

- 2.786 3.5
- 0.0004 x 3001
- 65 45.32 x 90
- 45.6 - 34.23
- 900.3/30.2450

Percent Error

- Percent error determines how accurate an

experimental value is compared quantitatively

with the correct or accepted value. - Percent error calculated by subtracting the

experimental value from the accepted value,

dividing the difference by the accepted value,

and then multiplying by 100

Percent Error

- Percent error Valueaccepted Valueexperimental

x 100 - Valueaccepted
- Percent error can have a positive or negative

value

Percent Error

- A student measures the mass and volume of a

substance and calculates its density as 1.40

g/mL. The correct, or accepted value of the

density is 1.36 g/mL. What is the percent error

of the students measurement? - 1.36g/mL 1.40 g/mL x 100 -2.9
- 1.36 g/mL

Percent Error

- What is your percent error from the lab when you

found the density of water? - 1.00g/mL g/mL x 100 -2.9
- 1.00 g/mL

Your experimental value

Percent Error pg. 45

- Two technicians independently measure the density

of a new substance. - Technician A Records 2.000, 1.999, 2.001 g/mL
- Technician B Records 2.5, 2.9, and 2.7 g/mL
- The correct value is found to be 2.701 g/mL.
- Which Technician is more precise? Which is more

accurate?

B

A

Go Through Answers on Packet

Directly Proportional

- Two quantities are directly proportional if
- Dividing one by the other gives a constant value
- y/x k
- k constant
- You can rearrange above equation by saying y

kx - If one increasesthe other increases at the same

rate (doubling one constant doubles the othr - 2y/2x k (constant)

Directly Proportional

All directly proportional relationships produce

linear graphs that pass through the origin

Inverse Proportions

- Two quantities are inversely proportional if
- Their product is constant
- xy k
- k constant
- The greater the speed less time to travel a

given distance - Double speed (2x) ½ required time
- Halving the speed (½) 2 times the time

Inverse Proportional

How Sweet It IsChemistry Lab

How Sweet It Is Lab

- Benedicts Solution Water Bath Test
- Results
- Beverages should have tested positive if they had

a sugar sweetener - Beverages should test negative if they had an

artificial sweetener

How Sweet It Is Lab

- What beverages tested positive?
- What beverages tested negative?
- Evaluate against labels on Sodas

How Sweet It Is Lab

- What did you notice about the densities of the

solutions? - Which ones had artificial sweeteners? Densities

less than one? - Which ones had natural sugar sweeteners?

Densities more than one?

How Sweet It Is Lab

- Analysis Questions
- 1. Evaluate the results against the labels on

the soda? Record actual sweeteners on a table in

your lab write-up. - How accurate were your results?

How Sweet It Is Lab

- Analysis Questions
- 2. Which sample do you think had the

highest/lowest sugar content? Explain why you

think this.

How Sweet It Is Lab

- Application Questions
- 1. How could you prove that carbonated water

contains no sweetener?

How Sweet It Is Lab

- Application Questions
- How could you determine a regular/diet soda by

using density and not opening the can? - Immerse in waterwhich one will sinkwhich one

will float?