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**Scientific Measurement and Significant Figures**

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**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

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**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

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**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 5.4 X 10-3 Proper Notation – One number to the left of the decimal

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**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”

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**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

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**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

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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 cm 2.54 cm in Choose the conversion factor that puts what you are converting to over what you are converting from

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**Conversion Examples $12.00 to quarters 56 yards to feet**

67 dimes to quarters 18.57 kg to mg 19.84 ft to m mL to L 48 quarters 168 feet 26.8 quarters 1.857 X 107 mg 6.047 m 12.45 L

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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

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**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

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**Making Sense of Measurements**

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex: Scientists want to be BOTH

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**Making Sense of Measurements**

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex: Scientists want to be BOTH

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**Making Sense of Measurements**

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex: Scientists want to be BOTH

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**Making Sense of Measurements**

Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex: Scientists want to be BOTH

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**Reading for Significance**

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Correct Measurement? 11.6 cm cm 11.65 cm

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**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.

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**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 sig figs.

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**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 sig figs. SIGNIFICANCE SANDWICH Zeros between two significant figures are significant

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**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: m sig figs. m sig figs. m sig figs. REASON: These zeros show SPECIFICITY of the measurement – they show the accuracy

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**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 m --- only 3 sig figs Both numbers can be written in a different form without sacrificing accuracy. HOW? Scientific Notation

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**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.

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**SIG FIG Practice Measurement # Significant Figures 10.01 m 10.0 m 10 m**

km L 56 crickets

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**Math and Significant Figures**

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

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**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 m m = m Since 1.34 only has 2 decimal places, you must round your answer to 2 decimal places ACTUAL ANSWER = 3.91 m

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**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 = 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

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**PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg =**

25.0 m x m = cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 25.0 m km = 68.7 m 2.20 g/cm3 307 kg 2.50 X 103 m2 7 cm cm3 25025 m OR 25.0 km (must be same units)

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