Unit 2: Measuring and CalculatingChapter 2

“1000 grams...well it sounded like a lot when i orderd it. ah well, I cant make hide nor hair of these metric boobytraps” My car gets

fourty rods to the hogshead and that's the

way I like it

Objectives

By the end of this unit, you will be able to: Distinguish between qualitative and quantitative

characteristics List three requirements for making a measurement List and define the seven basic SI units with their

categories of measurement Define the commonly used SI prefixes Define mass, weight, balance, and state the

difference between mass and weight Define temperature and give the basis for the

Celsius temperature scale Distinguish accuracy and precision

Objectives cont.

Define significant digits and counting numbers and determine the number of significant digits in a given measurement

Express results of math equations in significant digits

Convert numbers from decimal to scientific notation

Combine SI units to form derived units Demonstrate use of logic to solve problems Use the factor-label method to solve problems Define density and perform calculations using

density, mass, and volume

The International System (SI)

Qualitative measurement – a description with no measurement Color Smell

Quantitative measurement- a description with numerical information Length Mass

SI System continued…

Three requirements for quantitative measurement

1. We must know exactly what property we are trying to measure

2. We must have some standard with which to compare whatever we are measuring

3. We must have some method of making this comparison

SI System continued…

The SI system is the standard measuring system used in science SI is a modified version of the metric

system Most countries use SI or are

converting to it The SI system is very simple and

consistent The SI system has seven basic units…

Seven Basic Units of SIQuantity Unit Unit Symbol

Length Meter m

Mass Kilogram kg

Time Second s

Electric Current

Ampere A

Temperature Kelvin K

Amount of substance

Mole Mol

Luminous intensity

Candela cd

SI prefixes

In SI, prefixes are added to the base units to obtain different units of a convenient size for measuring larger or smaller quantities Kilometer = 1000 meters Millimeter = 1/1000 of a meter You will need to memorize the metric

prefixes and the values which they stand for

Next, a table of the metric prefixes…

SI PrefixesPrefix Symbol Meaning Multiplier

Mega M Million 1,000,000

Kilo K Thousand 1,000

Deci d Tenth 0.1

Centi c Hundredth 0.01

Milli m Thousandth 0.001

Micro µ Millionth 0.000001

Nano n Billionth 0.000000001

Pico p Trillionth 0.000000000001

Homework

Worth a possible 5 pointsDue:

Mass and Weight

What's the difference? Weight is a measure of the force of

gravity between two objects On objects weight on Earth can change

when the distance between the object and the center of the Earth changes

Mass is a measure of the amount of matter an object has Mass never changes

Mass

The SI unit for mass is the kilogram In the lab, we usually use the gram

(g), because a kilogram is too large The mass of a paperclip is about 1.5 g

The Balance The balance is the tool used to

measure mass Using the balance

Length

Length is the distance covered by a line segment connecting two pointsThe SI unit for length is the meter (m)Length is usually measured with a ruler or similar deviceExamples A nickel has a diameter of ~2 cm A notebook is about 25 cm long

Time

Time is the interval between two occurrencesThe SI unit for time is the second (s)Time is usually measured with a clock or watch The atomic clock is the most accurate

tool for measuring time

TemperatureThe temperature of a sample of matter is a measure of the average kinetic energy of the particles that make up the sample The greater the kinetic energy, the higher the

temperature

Temperature is usually measured with a thermometerThe SI unit for temperature is the Kelvin (k)The Celsius scale is also often used The Celsius scale is based on the boiling point and

freezing point of water It is related to the Kelvin scale. More later…

Accuracy Vs. Precision

Accuracy refers to how close a measurement is to the true or correct value for the quantityPrecision refers to how close a set of measurements for a quantity are to one another, regardless of whether the measurements are correct Usually measurements that have precision

are also accurate, but not always

Assignment

Complete Exercises 1-2 on page 19 of your textComplete Exercises 3-4 on page 23 of your textThis assignment is worth 10 pointsDue: By the end of class

Significant Digits (Sig Fig’s)

All digits that occupy places for which actual measurement was made are referred to as significant digits The places actually measured include one

uncertain, or estimated digit See Figure 2-7 in your text

Sig Fig’s cont.

The exactness of measurements is very important This is determined by the number of

significant digits in the measurement

There are a few rules for determining the number of significant digits in a recorded measurementCounting numbers (an exception) When something is counted (not measured) it

is considered to have an infinite amount of significant figures (more on that later)

Sig Fig Rules1. Digits other than zero are always significant

96 g 2 sig figs61.4 3 sig figs0.52 2 sig figs

2. One or more final zeros used after the decimal point are always significant

4.7200 km 5 sig figs8.0 2 sig figs

3. Zeros between two other significant digits are always significant

5.029 m 4 sig figs

4. Zeros used solely for spacing the decimal point are not significant

7000 g 1 sig fig0.00783 kg 3 sig figs

PracticeHow many significant digits in each of the following? 30.4 2700 5.10 0.023 7.0200 0.04010 3.00 2.700 0.0304 51.0

Assignment

Complete Exercise 5 on page 24 of your textThis assignment is worth 5 pointsDue: Tomorrow

Pop Quiz!!!Write the correct number of sig figs for the following:

1. 320 g 11. 1234 meters2. 32.0 m 12. 100,000 cd3. 0.0045 kg 13. 504.0032 g4. 50,000.0 L 14. 9.8 km5. 2.340 cm 15. 100.0001 pm6. 756 dm 16. 300 g7. 100 g 17. 5.34 ML8. 0.000500 L 18. 34 L9. 1.096 mL 19. 0.001 g10. 11.506 cg 20. 50 pencils

Scientific NotationScientific Notation makes it easier to work with large numbersIn Scientific Notation all numbers are expressed as the product of a number between 1 and 10 and a whole-number power of 10 M x 10n

1,000 = 1 x 103

Using Scientific Notation also makes counting sig figs easier 8000 = 8 x 103 1 sig fig 8000.0 = 8.0000 x 103 5 sig figs

Scientific Notation Practice

Convert the following to scientific notation 30,000 1,567 0.000000340 5.67 7,500,000

Scientific Notation RulesTo determine the number of digits that should appear in the answer to a calculation, we use two rules

1. In addition and subtraction, the answer may contain only as many decimal places as the measurement having the least number of decimal places 5.44 + 3.1 = 8.5 This answer should then be rounded off to the nearest tenth,

so the answer would be 8.52. In Multiplication and division, the answer may contain

only as many significant digits as the measurement with the least number of significant digits 1.1 x 2.000 = 2.200 You can only have 2 significant digits, so your answer would

be 2.2

Assignment

Complete Exercises 6-12 on page 27 of your text This will be worth a possible 10 points Due: Tomorrow

Derived UnitsBy combining SI units, we can obtain measurement units to express other quantities Distance divided by time = speed Length x Length = area

Unit of area is the square meter (m2) Area x Length = volume

Unit of volume is the cubic meter (m3) Most often in lab we use the milliliter (mL) for

volume 1000 cm3 = 1000 mL = 1 L = 1 (dm3)

Problem Solving

3 part method for solving problems

1. Decide what information is given2. Decide what information is needed3. Find a “bridge” that can help you

use the information that you have to obtain the information that you need The “bridge” is the information that you

will learn studying chemistry

Conversion Factors

A conversion factor is a ratio equivalent to one Convert 72 cm to meters

100 cm = 1 meter 100 cm/100cm = 1m/100cm; therefore

1m/100cm is your conversion factor 72cm x 1 = 72cm x (1m/100cm) So, 72cm = 72m/100 = 0.72 m

Convert 5.5 L to ml

Conversion Factors Cont.

Vertical bar To make conversions easier, we can

set off each factor by a vertical bar Convert 5 dm3 to cm3

Factor Label Method

In the factor label method, units are treated as factors, and as such, can be divided outExample on board

Density

Density is mass per unit of volume Density = mass/volume D=m/v Unit is g/ml

Assignment

Complete Exercises 13-24 on pages 30-31 Exercises 29, 32, 38, and 39 on page

32 of the text Exercises 44, 45,46 on page 35 of

your text Worth 20 points Due: Monday

Chapter Review

Complete chapter review questions

48 all, 49a, 50 all, 51 all, 54, 55, 57, 59, 60, 61, 62, 64, 65, 66 all, 68 all, 69 all, 70, 71 all, 73 all, 83, 85, 86, 94, and 95 on pages 36-38 of your text

Remember, these questions will be very similar to those found on the unit test, so do them all

This will be collected for a possible 25 points