Measurements

Measurements: Definitions

• Measurement: – comparison between measured quantity and

accepted, defined standards (SI)

• Quantity: – property that can be measured and described

by a pure number and a unit that names the standard

Measurement

• Types:– Qualitative:

• describe a substance without using numbers (measurements).

– Quantitative: • require measurement to be made and have to be

described by a QUANTITY (number and unit)

Measurement Requirements

• Know what to measure

• Have a definite agreed upon standard

• Know how to compare the standard to the measured quantity (tool)

Types of measurement

• Quantitative- – use numbers + units to describe the measured quantity.

Examples: the density of iron is 7.8 g/cm3.

• Qualitative- – use description (language) without numbers to describe

the measurement

• Quantitative or qualitative?– 4 feet _____________________– extra large _____________________– Hot _____________________– 100ºF _____________________

Measuring

• Numbers without units are meaningless.

• The measuring instrument limits how good the measurement is

Scientific Notations

• A shortcut method for writing very large and very small numbers using powers of ten

602,000,000,000,000,000,000,000,000

• The number is written as M x 10n

– n is + number = large numbers (>0)– n is - number = small numbers (<0)

Accuracy, Precision, and Certainty:

How good are the measurements?

Accuracy

how close the measurement is to the actual value

Precision

how well can the measurement be repeated. (How well do the measurements agree

with each other?)

Let’s use a golf anaolgy

Accurate? No

Precise? Yes

Accurate? Yes

Precise? Yes

Precise? No

Accurate? Maybe?

Accurate? Yes

Precise? We cant say!

In terms of measurement

• Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across.

• Were they precise?

• Were they accurate?

Assessing Uncertainty

• The person doing the measuring should asses the limits of the possible error in measurement

Significant figures (sig figs)

• How many numbers mean anything

• When we measure something, we can (and do) always estimate between the smallest marks.

21 3 4 5

Significant figures (sig figs)

• The better marks the better we can estimate.

• Scientist always understand that the last number measured is actually an estimate

21 3 4 5

Significant Digits and Measurement

• Measurement– Done with tools– The value depends on the smallest

subdivision on the measuring tool

• Significant Digits (Figures): – consist of all the definitely known digits plus

one final digit that is estimated in between the divisions.

Sig Figs

• Only measurements have sig figs.

• Counted numbers are exact

• A dozen is exactly 12

• A piece of paper is measured 11 inches tall.

• Being able to locate, and count significant figures is an important skill.

Measured Value

Uncer- tainty

Ruler Division

Known digits

Estimated digit

1.07 cm +/-0.01 cm 0.1 cm 1, 0 7

3.576 cm +/-0.001 cm 0.01 cm 3,5,7 6

22.7 cm +/- 0.1 cm 1 cm 2, 2 7

Significant Figures: Examples

Significant Rules examples

• What is the smallest mark on the ruler that measures 142.15 cm?– ____________________

• 142 cm?– ____________________

• 140 cm?– ____________________

• Does the zero count?• We need rules!!!

Rules of Significant Figures

Pacific: If there is a decimal point present

start counting from the left to right until encountering the first nonzero digit.

All digits thereafter are significant.Atlantic:

If the decimal point is absentstart counting from the right to left until

encountering the first nonzero digit. All digits are significant.

Sig figs.

How many SF in the following measurements?

1. 458 g

2. 4085 g

3. 4850 g

4. 0.0485 g

5. 0.004085 g

6. 40.004085 g

Sig Figs.

7. 405.0 g

8. 4050 g

9. 0.450 g

10.4050.05 g

11.0.0500060 g

Rounding rules

Look at the number next to the one you’re rounding.

0 - 4 : leave it

5 - 9 : round up

Round 45.462 to:

a) four sig figs

b) three sig figs

c) two sig figs

d) one sig fig

Calculations with Significant Figures

Multiplication and Division

Same number of sig figs in the answer as the least in the question

1) 3.6 x 653 = 2350.8

3.6 has 2 SF

653 has 3 SF

• answer can only have 2 SF

Answer: 2400

Multiplication and Division

• Same rules for division

• practice

• 4.5 / 6.245

• 4.5 x 6.245

• 9.8764 x .043

• 3.876 / 1983

• 16547 / 714

Practice

• 4.8 + 6.8765• 520 + 94.98• 0.0045 + 2.113• 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28• 6.7 - .542• 500 -126

• 6.0 x 10-2 - 3.8 x 10-3

The Metric System: SI System

An easy way to measure

The Metric System

• Easier to use because it is a decimal system

• Every conversion is by some power of 10.

• A metric unit has two parts– A prefix and a base unit.

• prefix tells you how many times to divide or multiply by 10.

SI Prefixes

• Exa peta tera

• Giga mega kilo

• Hecta deca Unit

• Centi milli micro

• Nano pico femto

• Atto

• Check blackboard for details

Fundamental Units

SI Unit Name Abbreviation

Length Meter M

Mass Kilogram Kg

Time Second s

Temperature Kelvin K

Electric current

Ampere A

Quantity of matter

Mole Mol

luminosity Candela Cd

Mass

• Quantity of matter

• The same in the entire universe

• Based on Pt/Ir alloy standard

• 1gram is defined as the mass of 1 cm3 of water at 4 ºC.

• 1000 g = 1000 cm3 of water at 4 ºC

• 1 kg = 1 L of water 4 ºC

Measuring Temperature

• Celsius scale.

• water freezes at 0ºC

• water boils at 100ºC

• body temperature 37ºC

• room temperature 20 - 25ºC

0ºC

Measuring Temperature

• Kelvin starts at absolute zero (-273 º C)• degrees are the same size• C = K -273• K = C + 273• Kelvin is always bigger.• Kelvin can never be negative. • Absolute zero: temp. at which a system

cannot be farther cooled.