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Measurement & Calculation

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Measurement & Calculation

An Introduction

Scientific Inquiry: What it is & What it is not!

- Scientific Notation- numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.
- 3,400 m = 3.4 x 103 m .0034 m = 3.4 x 10-3 m
- In addition/subtraction, exponents (n) must be equivalent
- In multiplication, exponents (n) are added.
- In division, exponents (n) are subtracted.

- Addition/Subtraction5.2 x 106 L9.3 x 10-4 J
- + 3.1 x 106L - 7.1 x 10-4 J
- 8.3 x 106 L2.2 x 10-4 J

Multiplication/Division (9.0 x 104 m)(6.0 x 102m)

54 x 106 m2

5.4 x 107m2

36 x 10-3 m /6.0 x 106 s

6 x 10-9 m/s

ApplyingUsing knowledge to solve

complex problems; inventing

InferringPredicting patterns based on data

formulating models; theorizing

RelatingCause and effect relationships; space/time

relationships; controlled experimentation

OrganizingCategorizing, grouping, classifying

Ordering: seriating and sequencing

ComparingSensory comparisons, relative position comparisons; measurement (linear, volume, mass, quantity, temperature)

CommunicatingSilent, oral, written, pictorial

Observing Seeing, hearing, feeling, tasting, smelling

Earth is center of universe

Claudis Ptolemy

Sun is center of Universe

Nicolas Copernicus

A.D. 150

1543

- Does size matter REALLY?!!

What items require exact measurement to you?

Quantity: Something that has magnitude, size, or amount

- 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 quantity made in the same way.

Name some predictions-

Percent error is calculated by subtracting the e xperimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100.

Percent Error = Valueaccepted – Valueexperimentalx 100

Valueaccepted

- http://www.youtube.com/watch?v=9PeVHnjqbBc

Significant Figures- numbers in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

Rules on Significant Figures-

Non-zero numbers are significant (83.45)

Captured zeros are significant.

(bordered by nonzero numbers- like 703)

Trailing zeros are significant IF there is a decimal (2.60; 400; 401.)

Leading zeros are never significant (00.016)

Identify the number of significant figures:

1) 3.0800

2) 0.00418

3) 7.09 x 10¯5

4) 91,600

5) 0.003005

6) 3.200 x 109

7) 250

8) 780,000,000

9) 0.0101

10) 0.00800

1)5

2)3

3)3

4)3

5)4

6)4

7)2

8)2

9)3

10)3

11) 13.01 + 10.1 = a. 23b. 23.1c. 23.11

12) 20.5 – 6.33 =a. 15b. 14.2c. 14.23

13) 22.1 + 14.2 =a. 30b. 36c. 36.3

14) 1.5 x 2 =a. 3b. 3.0c. 3.00

11) b.

12)b

13)c

14)a

Addition & Subtraction

Multiplication & Division

- When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.
- Ex. 13.55 – 4.3 = 9.25 = 9.2 (round)
- Whole numbers should be rounded so that the answer’s final digit should be rounded the same as that of the leftmost uncertain digit regardless of the number of places.

- http://www.youtube.com/watch?v=5UjwJ9PIUvE&feature=related

First determine the significant figures of the numbers of the problem. The least significant figure determines the number of significant figures in the product or quotient.

Ex. 237/6 = 39.5 = 40

- Addition/subtraction- when adding or subtracting decimals, the answer must have the same places as the least significant figure. You cannot produce a more accurate number than you started!
Ex. 6.32 g8.0 g

+ 1.2 g - 7.2 g

- Multiplication/division
- The answer can have no more significant figures than are in the measurement with the fewest number of significant figures.
- Ex. 1.10 mm x 6.0 mm =

6.6 mm2 because 6.60 mm2 is more precise than our measurements indicate.

7.5 g 0.8 g

- Base Units
- Length- mmeterm
- Masskgkilogramkg
- Timetseconds
- TemperatureTKelvinK
- Amount of substancenmolemol
- Electric current lampereA
- Luminous intensity Ivcandelacd

How many meters tall is Sherron Collins?

How many centimeters tall is Collins?

Can you convert between units?

He is 5’11” tall. There are 39” in a meter. There are 12” in a foot.

The answer: He is 71” tall which is 1.32 m . How many cm?

- What the difference between weight & mass?

Picture of Earth & Moon as seen from Mars!

Weight- measure of the gravitational pull on matter

Mass- measure of the quantity of matter in a substance

- Derived units are combinations of the SI base quantities.
- Volume is the amount of space occupied by a substance.
- Some combination units have their own name:
- Heat measurement:
- Joule= force x lengthnewton * m

- Pressure measurement:
- Pascal=Pa= force/area
- newton/m2 = kg/m * s2

- Heat measurement:

QuantitySymbolUnitDerivation

AreaAm2length x width

VolumeVm3 length x width x height

DensityD kg/m3 mass/volume

Molar massM kg/molmass/amt of sub.

Concentrationc mol/Lamt of sub./volume

Molar volumeV m3/molvolume/amt of sub.

EnergyE Jouleforce x length

Note: mol = mole

Area= length x width

2 cm x 8 cm = 16 cm 2

2 cm

8 cm

6 m

2 m

Volume = length x width x height

4m x 2m x 6m=

48 m3

4 m

6 m

2 m

4 m

24 kg = 0.5 kg/m3

4m x 2m x 6m

Density = mass/volume

24 kg

Molar mass = mass

amt. of sub.

8 kg = 2 kg

4 mol mol

8 kg

4 moles of NaCl

Concentration=

Amt. of sub

volume

3 mol = 3 mol

1 LL

3 moles Co

1000 ml

0.4 moles

caffeine

Molar Volume=

volume

amt of substance

0.4 L = 1 L

0.4 mol mol

0.4 L

Density= Mass

Volume

http://www.youtube.com/watch?v=fqLCwuKMBMA

1 dozen donuts = 12 donuts

If I had 3 dozen donuts, how many donuts do I have?

3 dozen| 12 donuts = 36 donuts

1 dozen

If I had 48 donuts, how many dozen donuts do I have?

48 donuts|1 dozen=4 dozen donuts

12 donuts

- A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other.
- Always go back to the units you know well
- Use LOGIC!

1 m = 100 cm = 0.001 km How many km is it to KU if you are 7800 m away?

1 L = 1000 ml = 100 clHow many ml are in 6.2 L of Mt. Dew?

1 kg = 1000 g = 1,000,000 mg How many g are in 500,000 mg?

7.8km

6200 ml

500 g

- Direct Proportional- 2 quantities are directly proportional to each other if dividing one by the other gives a constant value
- y = k
- X

- Inverse Proportionality-
- 2 quantities if their product is constant
- Example: xy = k