What You’ll Learn in this Unit Significant Figures Scientific Notation Measurement Dimensional

Analysis Error Density Graphical analysis

Review of Measurement Terms Qualitative measurements -

words Quantitative measurements –

involves numbers (quantities) Depends on reliability of

instrument Depends on care with which it is

read

Precision vs. Accuracy

Precision- the degree of agreement among several measurements of the same quantity.

Accuracy- the agreement of a particular value with the true value

Uncertainty Basis for significant figures All measurements are

uncertain to some degree Random error - equal chance

of being high or low- addressed by averaging measurements - expected

Significant Figures Meaningful digits in a

measurement The number of significant

figures in your measurement will tell the reader how exact the instrumentation used

If it is measured or estimated, it has sig figs.

If not it is exact (e.g. 5 apples).

Significant Figures

All numbers 1-9 are significant. The problem are the ZEROS. Which ones count and which don’t? In between numbers 1-9 does Example: 4001……… has 4 sig

figs Now let me tell you a story…

Left handed Archer

There once was a left handed archer who loved to shoot decimals. Zeros could not stop his arrow but numbers could.

If there is a decimal in the number begin on the left. Go through any zeros, come to the first number then all other numbers that follow are SIGNIFICANT!

→0.0040 →50.401

No decimals

If a number has no decimals you begin on the right hand side.

Go through any zeros , come to the first number.

Then all numbers after that count

5000← 405,000 ←

Doing the Math

Multiplication and division, same number of sig figs in answer as the least in the problem

Addition and subtraction, same number of decimal places in answer as least in problem.

Scientific Notation

100 = 1.0 x 102

0.001 = 1.0 x 10-3

-- This provides a way to show significant figures.

TOO QUICK FOR YOU!

So here are the rules.. slowly!1. Place decimal point after 1st

real non-zero integer. (ex) 1.0 NOT 10.0

2. Raise 10 to the exponential which equals the number of places you moved.

Scientific Notation

The product of 2.3 x 10 x 10 x 10 equals 2300 (2.3 x 103)

Note: Moving the decimal to the left will

increase the power of 10 Moving the decimal to the right will

decrease the power of 10

Sample Problems

2387 0.00007031 2900000000 0.008900 90100000 0.00000210

Answers

2.387 x 103

7.031 X 10-5

2.9 x 109

8.900 X 10-3

9.01 X 107

2.10 X 10-6

Scientific Notation Multiplication and Division

Use of a calculator is permitted use it correctly No calculator? Multiply the

coefficients, and add the exponents

(3 x 104) x (2 x 102) =

(2.1 x 103) x (4.0 x 10-7) =

6 x 106

8.4 x 10-4

Scientific Notation

Multiplication and Division• In division, divide the coefficients,

and subtract the exponent in the denominator from the numerator

3.0 x 105

6.0 x 102= 5 x 102

Scientific Notation

•Addition and Subtraction

•Before numbers can be added or subtracted, the exponents must be the same

•Calculators will take care of this

•Doing it manually, you will have to make the exponents the same- it does not matter which one

you change. (6.6 x 10-8) + (4.0 x 10-9) =

(3.42 x 10-5) – (2.5 x 10-6) =

7 x 10-8

3.17 x 10-5

Measurement

Every measurement has two parts

Number with the correct sig - figs

Scale (unit) We use the

Systeme Internationale (SI).

COMMON SI UNITS

Symbol   Unit Name   Quantity   Definition

   m meter length base unit

   kg kilogram mass base unit

   s second time base unit

   K kelvin temperature    base unit

   °Cdegree Celsius**  

temperature

   m3 cubic meter volume m3

   L liter** volume dm3 = 0.001 m3

   N newton force kg·m/s2

   J joule energy N·m

   W watt power J/s

   Pa pascal pressure N/m2

   Hz hertz frequency 1/s

Metric Base Units

•Mass - kilogram (kg)•Length- meter (m)•Volume- (L)•Time - second (s)•Temperature- Kelvin (K)•Electric current- ampere (amp, A)•Amount of substance- mole (mol)•Energy – joule (j)

Prefixesgiga- G 1,000,000,000 109

mega - M 1,000,000 106

kilo - k 1,000 103

deci- d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro- 0.000001 10-6

nano- n 0.000000001 10-9

Dimensional Analysis

Using Units to solve problems

Dimensional Analysis

Use conversion factors to change the units

Conversion factors = 1 1 foot = 12 inches (equivalence

statement) 12 in = 1 = 1 ft.

1 ft. 12 in

2 conversion factors multiply by the one that will give you the

correct units in your answer.

Example Problem

The speed of light is 3.00 x 108 m/s. How far will a beam of light travel in 1.00 ns?

Well, we know that 1.00 ns = 10-9 seconds

(3.00 x 108 m) X (10-9 s) = 3.00 x 10-9 m/ns

s (1.00 ns)

Example Problems

11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile The Kentucky Derby race is 1.25 miles.

How long is the race in rods, furlongs, meters, and kilometers?

A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?

Volume

The space occupied by any sample of matter

Calculated for a solid by multiplying the length x width x height

SI unit = cubic meter (m3) Everyday unit = Liter (L), which is

non-SI

Units of Mass Mass is a measure of the quantity of matter

Weight is a force that measures the pull by gravity- it changes with location

Mass is constant, regardless of location. The SI unit of mass is the kilogram (kg),

even though a more convenient unit is the gram

Measuring instrument is the balance scale

Density Which is heavier- lead or feathers? It depends upon the amount of the

material A truckload of feathers is heavier than a small pellet of lead

The relationship here is between mass and volume- called Density

Density Ratio of mass to volume D = m/V Common units are g/mL, or

possibly g/cm3, (or g/L for gas) Useful for identifying a compound Useful for predicting weight An intensive property- does not

depend on what the material is

Things related to density density of corn oil is 0.89 g/mL

and water is 1.00 g/mL What happens when corn oil

and water are mixed? Why? Will lead float?

Example Problem

An empty container weighs 121.3 g. Filled with carbon tetrachloride

(density 1.53 g/cm3 ) the container weighs 283.2 g. What is the volume of the container?

Density and Temperature

What happens to density as the temperature increases? Mass remains the same Most substances increase in volume as temperature increases

Thus, density generally decreases as the temperature increases

Density and water Water is an important

exception Over certain temperatures, the

volume of water increases as the temperature decreases

Does ice float in liquid water? Why?

Specific Gravity

A comparison of the density of an object to a reference standard (which is usually water) at the same temperature Water density at 4 oC = 1 g/cm3

Formula D of substance

(g/cm3) D of water

(g/cm3)• Note there are no units left, since they

cancel each other• Measured with a hydrometer • Uses?

• Gem purity• differentiating between different types of

crude oils/gasoline• urine tests for concentration of all chemicals

in your urine

Specific gravity =

Temperature

Heat moves from warmer object to the cooler object Glass of iced tea gets colder?

Remember that most substances expand with a temperature increase?

Basis for thermometers

Temperature scales

Celsius scale- named after a Swedish astronomer Uses the freezing point (0 oC) and boiling point (100 oC) of water as references

Divided into 100 equal intervals, or degrees Celsius

Temperature scales

Kelvin scale (or absolute scale) Named after Lord Kelvin K = oC + 273 A change of one degree Kelvin is the same as a change of one degree Celsius

No degree sign is used

Temperature scales

Water freezes at 273 K Water boils at 373 K 0 K is called absolute zero, and

equals –273 oC

Temperature

A measure of the average kinetic energy

Different temperature scales, all are talking about the same height of mercury.

In lab take the reading in ºC then convert to our SI unit Kelvin

ºC + 273 = K

100ºC = 212ºF0ºC = 32ºF

100ºC = 180ºF1ºC =

(180/100)ºF1ºC = 9/5ºF

Example problem

A 55.0 gal drum weighs 75.0 lbs. when empty. What will the total mass be when filled with ethanol?

density 0.789 g/cm3 1 gal = 3.78 L

1 lb = 454 g

Error Calculations

Error = Experimental value- accepted value

% error = [error] accepted value

X 100

Graphing

The relationship between two variables is often determined by graphing

A graph is a “picture” of the data

Graphing Rules – 10 items1. Plot the independent variable on the x-axis

(abscissa) – the horizontal axis. Generally controlled by the experimenter

2. Plot the dependent variable on the y-axis (ordinate) – the vertical axis.

3. Label the axis. Quantities (temperature, length, etc.) and

also the proper units (cm, oC, etc.)

4. Choose a range that includes all the results of the data

Graphing Rules

5. Calibrate the axis (all marks equal)

6. Enclose the dot in a circle (point protector)

7.Give the graph a title (telling what it is about)

8. Make the graph large – use the full piece of paper

9. Indent your graph from the left and bottom edges of the page

10. Use a best fit line, do not connect points