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 Prefix Symbol Value kilo k 103 deci d 10-1 centi c 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.

1) All non-zeros are significant Ex: 23 m --- 2 sig figs. Rules for Determining the Number of Significant Figures in a Given Measurement 1) All non-zeros are significant Ex: 23 m --- 2 sig figs.

2) Zeros between non-zeros are significant Ex: 203 m --- 3 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

3) Zeros after a decimal AND after a non-zero 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

4) Zeros that act as PLACE HOLDERS only are NOT significant. 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 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)