Lecture 01 Measurements
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This document discusses measurement and significant figures. It defines physical quantities, units of measure, and the seven fundamental units. It also discusses converting between units, estimating measurements, and determining the number of significant figures in calculations and measurements based on the precision of the values. Calculations must account for the least precise measurement or factor. Measurements are rounded based on the smallest number of decimal places in any term in the calculation.
Lecture 01 Measurements
- 1. Measurement and Significant Figures
- 2. Electric ChargeLengthTimePhysical QuantitiesA physical quantity is a quantifiable or assignable property ascribed to a parti- cular phenomenon, body, or substance.
- 3. Measuring diameter of disk.Units of MeasureA unit is a particular physical quantity with which other quantities of the same kind are compared in order to express their value. A meter is an established unit for measuring length.Based on definition, we say the diameter is 0.12 m or 12 centimeters.
- 5. Units for MechanicsIn mechanics we use only three fundamental quantities: mass, length, and time. An additional quantity, force, is derived from these three.
- 6. 12 in.1 in. = 2.54 cmExample 1:Convert 12 in. to centimeters given that 1 in. = 2.54 cm.Step 1: Write down quantity to be converted.Step 2. Define each unit in terms of desired unit.Step 3. For each definition, form two conversion factors, one being the reciprocal of the other.
- 7. 1 mi. = 5280 ft1 h = 3600 sExample 2:Convert 60 mi/h to units of ft/s given 1 mi. = 5280 ft and 1 h = 3600 s.Step 1: Write down quantity to be converted.Note: Write units so that numerators and denominators of fractions are clear.Step 2. Define each unit in terms of desired units.
- 8. Ex. 2 (Cont):Convert 60 mi/h to units of ft/s given that 1 mi. = 5280 ft and 1 h = 3600 s.Step 3. For each definition, form 2 conversion factors, one being the reciprocal of the other.1 mi = 5280 ft1 h = 3600 sStep 3, shown here for clarity, can really be done mentally and need not be written down.
- 9. Ex. 2 (Cont):Convert 60 mi/h to units of ft/s given that 1 mi. = 5280 ft and 1 h = 3600 s.Step 4. Choose Factors to cancel non-desired units.Treating unit conversions algebraically helps to see if a definition is to be used as a multiplier or as a divider.
- 10. 012Uncertainty of MeasurementAll measurements are assumed to be approximate with the last digit estimated.The length in “cm” here is written as:1.43 cmThe last digit “3” is estimated as 0.03 of the interval between 3 and 4.
- 11. 012Estimated Measurements (Cont.)Length = 1.43 cmThe last digit is estimated, but is significant. It tells us the actual length is between 1.40 cm and 1.50. It would not be possible to estimate yet another digit, such as 1.436.This measurement of length can be given in three significant digits—the last is estimated.
- 12. 0.0062 cm 2 significant figuresSignificant Digits and NumbersWhen writing numbers, zeros used ONLY to help in locating the decimal point are NOT significant—others are. See examples.4.0500 cm 5 significant figures0.1061 cm 4 significant figures50.0 cm 3 significant figures50,600 cm 3 significant figures
- 13. Example:The appropriate way to write the answer is:P = 7.0 N/m2Rule 1. When approximate numbers are multiplied or divided, the number of significant digits in the final answer is the same as the number of significant digits in the least accurate of the factors.Least significant factor (45) has only two (2) digits so only two are justified in the answer.
- 14. Rule 2. When approximate numbers are added or subtracted, the number of significant digits should equal the smallest number of decimal places of any term in the sum or difference.Ex: 9.65 cm + 8.4 cm – 2.89 cm = 15.16 cmNote that the least precise measure is 8.4 cm. Thus, answer must be to nearest tenth of cm even though it requires 3 significant digits.The appropriate way to write the answer is:15.2 cm
- 15. Round the following to 3 significant figures:Examples2.3452becomes 2.35becomes 0.08760.08757becomes 23,70023,650.01becomes 5.004.99502
- 16. Working with NumbersIn the classroom, we assume all given info is accurate to 3 signi- ficant figures.In lab, the number of significant figures will depend on limitations of the instruments.Classroom work and lab work should be treated differently unless told otherwise.
Editor's Notes
- #2: 1IT1