Data AnalysisChapter 2

What’s wrong with this sign?

Temperature

30°C 30°F

Système Internationale d’ Unités

SI unit

Prefixes used with SI units

English vs. Metric Units

Left Image: http://webapps.lsa.umich.edu/physics/demolab/controls/imagedemosm.aspx?picid=1167Right Image: http://share.lancealan.com/N800%20ruler.jpg

Which is longer?

A. 1 mile or 1 kilometer

B. 1 yard or 1 meter

C. 1 inch or 1 centimeter

1.6 kilometers

1 mile

1 yard = 0.9444 meters

1 inch = 2.54 centimeters

Metric Units of Length

The basic unit of length in the metric system in the meter and is represented by a lowercase m.

Metric Units

1 Kilometer (km) = 1000 meters

1 Meter = 100 Centimeters (cm)

1 Meter = 1000 Millimeters (mm)

Which is larger?

A. 1 meter or 105 centimeters

B. 4 kilometers or 4400 meters

C. 12 centimeters or 102 millimeters

D. 1200 millimeters or 1 meter

Measuring Length

How many millimeters are in 1 centimeter?

What is the length of the line in centimeters? _______cm

What is the length of the line in millimeters? _______mm

1 centimeter = 10 millimeters

What is the length of the line to the nearest centimeter? ________cm

English vs. Metric Units

Which is larger?

1. 1 Pound or 100 Grams

2. 1 Kilogram or 1 Pound

3. 1 Ounce or 1000 Milligrams

1 pound = 453.6 grams

1 kilogram = 2.2 pounds

1 ounce of gold = 28,349.5 milligrams

Metric Units of mass

Mass refers to the amount of matter in an object.

The base unit of mass in the metric system in the kilogram and is represented by kg.

Metric Units

1 Kilogram (km) = 1000 Grams (g)

1 Gram (g) = 1000 Milligrams (mg)

Which is larger?

A. 1 kilogram or 1500 grams

B. 1200 milligrams or 1 gram

C. 12 milligrams or 12 kilograms

D. 4 kilograms or 4500 grams

Kilogram Prototype Image - http://en.wikipedia.org/wiki/Kilogram

English vs. Metric Units

Which is larger?

A. 1 liter or 1 gallon

B. 1 liter or 1 quart

C. 1 milliliter or 1 fluid ounce

1 gallon = 3.79 liters

It would take approximately 3 ¾ 1-liter bottles to equal a gallon.

1 fl oz = 29.573 ml

1 12-oz can of soda would equal

approximately 355 ml.

1 quart = 0.946 liters

Metric Units

Volume is the amount of space an object takes up.

The base unit of volume in the metric system in the liter and is represented by L or l.

Metric Units

1 liter (L) = 1000 milliliters (mL)

1 milliliter (mL) = 1 cm3 (or cc) = 1 gram*

Which is larger?

A. 1 liter or 1500 milliliters

B. 200 milliliters or 1.2 liters

C. 12 cm3 or 1.2 milliliters*

Measuring Volume

We will be using graduated cylinders to find the volume of liquids and other objects.

Read the measurement based on the bottom of the meniscus or curve. When using a real cylinder, make sure you are eye-level with the level of the water.

What is the volume of water in the cylinder? _____mL

What causes the meniscus?

A concave meniscus occurs when the molecules of the liquid attract those of the container. The glass attracts the water on the sides.

Measuring Liquid Volume

Imag

es c

reat

ed a

t ht

tp:/

/ww

w.s

tand

ards

.dfe

s.go

v.uk

/prim

aryf

ram

ewor

k/do

wnl

oads

/SW

F/m

easu

ring_

cylin

der.

swfWhat is the volume of water in each cylinder?

Pay attention to the scales for each cylinder.

Measuring Solid Volume

10 cm

9 cm

8 cm

We can measure the volume of regular object using the formula length x width x height.

_____ X _____ X _____ = _____

http

://re

sour

ces.

edb.

gov.

hk/~

s1sc

i/R_S

1Sci

ence

/sp/

en/s

ylla

bus/

unit1

4/ne

w/te

stin

gmai

n1.h

tm

We can measure the volume of irregular object using water displacement.

Amount of H2O with object = ______

About of H2O without object = ______

Difference = Volume = ______

Temperature Scales

How hot? How cold? direction of Heat Transfer

Celsius – 0 0C Freezing Point of Water

100 0C Boiling Point of Water

Kelvin = C° + 273 No degree signs are used O Kelvin = -273.150 C

▪ coldest possible temperature

What is the metric unit for…?

Length – size meter (m)

Mass – amount of matter Kilogram (kg) or gram (g)

Volume – space something takes up Liter (l) or centimeters cubed (cm3)

Temperature – amount of heat Kelvin (K) = celsius + 273

Density

Measure of how much matter is squeezed into a given space

density = mass volume

Which one is more dense?

A block of wood and a block of steel have the same volume

What do you think?

What happens to the density of an object if it is cut into pieces?

Which has the greater density, a single uranium atom or Earth?

Scientific Notation

coefficient x 10 raised to a power

Single gram of hydrogen 602,000,000,000,000,000,000,000

molecules = 6.02 x 1023 molecules

Mass of an atom of gold 0.000000000000000000000327 grams

= 3.27 x 10-22 grams

Practice

36,000 3.6 x 104

503,000,000 5.03 x 108

0.00076 7.6 x 10-4

Significant Figures

The valid digits of a number  In measurement: includes all of the

digits that are known, plus a last digit that is estimated

Significant Figures

Significant: nonzero digits final zeros after the decimal points zeros between two other significant

digits

Not significant zeros used solely for spacing the decimal

point are not significant.

Examples

each have only two sig figs 0.0071 meter 0.42 meter 0.000099 meter

7.1 x 10-3 meter4.2 x 10-1 meter9.9 x 10-5 meter

Significant Figures

Value

5.60

5.6

0.012

0.0012003

0.0120

0.0012

# of significant figures

3

2

2

5

3

2

Rounding

If the digit immediately to the right of the last significant digit is less than 5, it is dropped 5 or greater - last significant digit

increased by 1 41.58 square meters 41.6 square

meters

Practice

Round 65.145 meters to 4 sig figs 65.15m

Round 100.1°C to 1 sig fig 100°C

Round 154 cm to 2 sig figs 150

Round 0.000718 kilograms to 2 sig figs 0.00072

Measurements with an Unlimited Number of Significant Digits

Counting Example: 23 people in the classroom

▪ (Not 22.9 or 23.1) 23.00000000……………….

Exactly defined quantities Example: 60 minutes = 1 hour

▪ 60.00000000……………………..

Calculation Rules

calculated answer cannot be too precise not more precise than the least precise

measurement

Multiplication and Division same number of sig figs as the

measurement with the least number of sig figs

Addition and Subtraction same number of decimal places as the

measurement with the least number of decimal places

Accuracy and Precision

Accuracy How close a

measurement comes to the actual value of what is being measured

Precision How close a series

of measurements are to one another

Error

Difference between accepted value and experimental value

error = experimental value – accepted value

% error = x 100% error

accepted value

Error

% error = x 100%

99.1°C – 100.0°C x 100% 100.0°C

0.9°C x 100% 100.0°C

0.9%

error

accepted value

=

=

=