Scientific Measurement and Significant Figures

Taking Measurements

Need for Standards Basis of comparison – allows for proper

communication of information if all are using the same system

Le Systeme International d’Unite’s (SI)

- International System

aka – The Metric System

SI Units – see page 26

Measurement Unit Abbreviation

Length Meter m

Mass Gram g

Volume Liter L

Temperature Kelvin (or Celcius)

K or (oC)

Number of Particles

Mole mol

Dealing With Very Large or Very Small Numbers

Scientific Notation Uses powers of 10 to represent the

magnitude of the number but keeping the same unit

BIG NUMBERS – positive exponents

Small numbers – negative exponents 23000 2.3 X 104

0.0054 5.4 X 10-3

Proper Notation – One number to the left of the decimal

Entering Scientific Notation into Your Calculator

Ex: 5.4 X1016

Step 1: Enter “5.4” Step 2: Hit “2nd” key Step 3: Hit “,” key (Second function is “EE”)

An “E” will appear Enter the exponent “16” Entered value should read “5.4E16” DO NOT USE “^” or “10^” or “10E”

Unit Multipliers Purpose: allow the measurement to use reasonable

numbers – make the numbers smaller or larger with a prefix in front of the unit to represent the magnitude (size) of the measurement

Ex. Measuring the mass of a whale

Prefix Symbol Value

kilo k 103

deci d 10-1

centi c 10-2

milli m 10-3

Converting Units

DIMENSIONAL ANALYSIS Changing from one unit to another unit

requires: 1) Same type of measurement

- you cannot convert length into mass 2) A conversion factor

Conversion Factors

Mathematical Ratio of the two units you are converting

Ex: Conversion of inches to centimeters 1 inch = 2.54 cm

Possible Conversion Factors 1 in or 2.54 cm

2.54 cm 1 in

Choose the conversion factor that puts what you are converting to over what you are converting from

Conversion Examples

$12.00 to quarters 56 yards to feet 67 dimes to quarters 18.57 kg to mg 19.84 ft to m 12 450 mL to L

48 quarters 168 feet 26.8 quarters 1.857 X 107 mg 6.047 m 12.45 L

Multiple Dimensions The number of dimensions determines the

number of conversions 12.5 m2 to cm2

Area is two dimensions (length x width) so two conversions are needed

25.0 ft3 to cm3

Conversions

1 L = 1000 mL 1 mL = 1 cm3; If its water, 1 mL = 1 g 1 Kg = 1000 g 1 g = 1000 mg 1 in = 2.54 cm

Making Sense of Measurements

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex:

Scientists want to be BOTH

Making Sense of Measurements

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex:

Scientists want to be BOTH

Making Sense of Measurements

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex:

Scientists want to be BOTH

Making Sense of Measurements

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex:

Scientists want to be BOTH

Reading for Significance

Correct Measurement? 11.6 cm 11.6283476 cm 11.65 cm

Significance of a Measurement

A Measurement can only be as accurate as the tool used to make it

A tool will allow for exact numbers plus one decimal place of estimation

These are known as SIGNIFICANT FIGURES

These determine the basis of your calculations – the more accurate your measurement, the more accurate your calculations.

Rules for Determining the Number of Significant Figures in a Given Measurement

1) All non-zeros are significant

Ex: 23 m --- 2 sig figs.

Rules for Determining the Number of Significant Figures in a Given Measurement

2) Zeros between non-zeros are significant

Ex: 203 m --- 3 sig figs. SIGNIFICANCE SANDWICH

Zeros between two significant figures are significant

Rules for Determining the Number of Significant Figures in a Given Measurement

3) Zeros after a decimal AND after a non-zero are significant Ex: 203.0 m --- 4 sig figs.

203.00 m --- 5 sig figs.

203.000000000 m --- 12 sig figs.

REASON: These zeros show SPECIFICITY of the measurement – they show the accuracy

Rules for Determining the Number of Significant Figures in a Given Measurement

4) Zeros that act as PLACE HOLDERS only are NOT significant.EX: 2030 m --- only 3 sig figs

0.00203 m --- only 3 sig figs

Both numbers can be written in a different form without sacrificing accuracy.

HOW?

Scientific Notation

Rules for Determining the Number of Significant Figures in a Given Measurement

5) Counting numbers, those that do not use a measuring device, are considered infinitely significant. Ex: 24 dogs Can’t get more accurate Only is important when they are used in a

calculation.

SIG FIG Practice

Measurement # Significant Figures

10.01 m

10.0 m

10 m

50050 m

56.610 g

0.008910 km

23.010 L

56 crickets

Math and Significant Figures

A calculation can only be as accurate as the least accurate part

Addition and Subtraction Rules for Sig Figs.

RULE: The answer can only have as many decimal places as the number with the

fewest decimal places. Ex. 1.34 m + 2.5678 m = 3.9078 m

Since 1.34 only has 2 decimal places, you must round your answer to 2 decimal places

ACTUAL ANSWER = 3.91 m

Multiplication and Division Rules for Sig Figs.

RULE: The answer can only have as many significant figures as the number with the

fewest significant figures. Ex: 8.97 m X 5.2 m = 46.644 m2

Since 5.2 m only has 2 significant figures, you must express your answer with the first two significant figures beginning from the left hand side.

ACTUAL ANSWER = 47 m2

PRACTICE

23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X

10.5 cm = 25.0 m + 25.0 km =

68.7 m 2.20 g/cm3

307 kg 2.50 X 103 m2

7 cm 2180000 cm3

25025 m OR 25.0 km

(must be same units)