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History of Measurement

History of Measurement. VFMS 2014 Mrs. Long. Measurement Notes. I. Historical units of measurement Length 1. Cubit = distance from the tip of the elbow to the tip of the middle finger. 2. Fathom = distance across a man’s

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History of Measurement

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  1. History of Measurement VFMS 2014 Mrs. Long

  2. Measurement Notes • I. Historical units of measurement • Length 1. Cubit = distance from the tip of the elbow to the tip of the middle finger. 2. Fathom = distance across a man’s outstretched arms. • 3. Span – distance from pinky to thumb on an outstretched hand. • 4. Digit – length of one finger.

  3. Measurement Notes • Weight • Babylonians improved upon the invention of the balance by establishing the world’s first weight standards – polished stones! • Egyptians & Greeks used a wheat seed as the smallest unit of weight.

  4. II. Timeline of measurement • Thirteenth century – King Edward of England, realized the importance of standardization – ordered the “iron ulna”. • 1793 – Napoleon’s rule of France, the metric system was born! Based on the meter – supposed to be one-ten–millionth (1/10,000,000 ) of the Earth’s circumference (measured at 40,000 km)

  5. II. Timeline of measurement • 1960 – Officially adopted Systeme International (SI System) need for universal language in sciences recognized. Decimal system is based on units of 10. • Today – Accepted & used worldwide by scientist

  6. III. Fundamental Units of Measurement

  7. Metric System • The metric system is based on a base unit that corresponds to a certain kind of measurement • Length = meter • Volume = liter • Weight (Mass) = gram • Prefixes plus base units make up the metric system • Example: • Centi + meter = Centimeter • Kilo + liter = Kiloliter

  8. IV. Using the Metric System To convert to a smaller unit, move the decimal point to the right or multiply. To convert to a larger unit, move the decimal point to the left or divide. Bigger Smaller

  9. Metric System • The three prefixes that we will use the most are: • kilo • centi • milli smaller than base unit LARGER than base unit

  10. Metric System • These prefixes are based on powers of 10. What does this mean? • From each prefix every “step” is either: • 10 times larger or • 10 times smaller • For example • Centimeters are 10 times larger than millimeters • 1 centimeter = 10 millimeters

  11. Metric System • If you move to theleftin the diagram, move the decimal to the left • If you move to the rightin the diagram, move the decimal to the right

  12. Example #1 13.2 mg = ? g Step 1: Identify that mg < g Step 2: slide decimal point to the left 3 times 13.2 mg Step 3: put a “0” in front of the decimal and add correct unit to the number 0.0132 g

  13. Example 2 5.7 km = ? cm Step 1: Identify that km > cm Step 2: slide decimal point to the right 5 times because kilometers are 5 units larger than centimeters 5.7 km Step 3: put four “0’s” in behind the 7 and add the correct unit to the number 570,000 cm

  14. Metric System 500 • Now let’s start from meters and convert to centimeters 5 meters = _____ centimeters • Now let’s start from kilometers and convert to meters • .3 kilometers = _____ meters 300

  15. Metric System • Review • What are the base units for length, volume and mass in the metric system? • What prefix means 1000? 1/10?, 1/1000? • How many millimeters are in 12.5 Hm? • How many Kiloliters are in 4.34cl?

  16. Metric System 4 • Now let’s start from meters and convert to kilometers 4000 meters = _____ kilometers • Now let’s start from centimeters and convert to meters • 4000 centimeters = _____ meters 40

  17. V. Accuracy vs. Precision 1. Accuracy – nearness of a measurement to the standard or true value. • Precision – the degree to which several measurements provide answers very close to each other. 3. Percent error: • a measure of the % difference between a measured value and the accepted “correct” value • formula: | correct – measured | x 100 = % error correct

  18. VI. Significant Figures- Certain vs. Uncertain Digits: • Certain – DIGITS THAT ARE DETERMINED USING A MARK ON AN INSTRUMENT OR ARE GIVEN BY AN ELECTRONIC INSTRUMENT • Uncertain – THE DIGIT THAT IS ESTIMATED WHEN USING AN INSTRUMENT WITH MARKS (ALWAYS A ZERO OR FIVE – FOR THIS CLASS)

  19. Significant figures • Rules • Numbers other than zero are always significant • 96 ( 2 ) 61.4 ( 3 ) • One or more zeros used after the decimal point is considered significant. • 4.7000 ( 5 ) 32 ( 2 ) • Zeros between numbers other than zero are always significant. • 5.029 ( 4 ) 450.089 ( 6 )

  20. Zeros used at the end or beginning are not significant. The zeros are place holders only. • 75,000 ( 2 ) 0.00651 ( 3 ) • Rule for rounding-If the number to the right of the last significant digit is 5 or more round up. If less than 5, do not round up. • Need 2 sig figs. For this value 3420 (3400 ) • Need 3 sig figs. For this value 0.07876 ( 0.0788)

  21. Significant Figures • Digits in a measured number that include all certain digits and a final digit with some uncertainty

  22. Addition and Subtraction- answer may contain only as many decimals as the least accurate value used to find the answer. 33.014+ 0.01 = 33.02 • Multiplication and Division- answer may contain only as many sig. Figs. As the smallest value used. 3.1670 x 4.0 = 12.668 13

  23. Example State the number of significant figures in the following set of measurements: a. 30.0 g b. 29.9801g c. 0.03 kg d. 31,000 mg e. 3102. cg

  24. VII. Scientific Notation Scientific notation Representation of a number in the form A x 10n • Scientists work with very large and very small numbers. In order to make numbers easier to work with, scientists use scientific notation. • Scientific notation- there must always be only one non-zero digit in front of the decimal.

  25. In scientific notation, the number is separated into two parts. The first part is a number between 1 and 9. The second is a power of ten written in exponential form. • Examples: 100= 10x10= 102 1000= 10x10x10=103 0.1=1/10=10-1 .01=1/100=1/10x1/10=10-2

  26. Converting numbers to Scientific notation • To write numbers in scientific notation, the proper exponent can be found by counting how many times the decimal point must be moved to bring it to its final position so that there is only one digit to the left of the decimal point (the number is between 1 and 9). • A(+) positive exponent shows that the decimal was moved to the left. It is moved to the right when writing the number without an exponent. • A (-) negative exponent shows that the decimal was moved to the right. It is moved to the left to get the original number.

  27. Another method of deciding if the exponent is positive or negative is to remember that values less than one (decimals) will have negative exponents and values of one or greater than one have positive exponents. • Examples: 920=9.2x100=9.2x102 1,540,000=1.54x1,000,000=1.54x106 83500=8.35x10,000=8.35x104 0.018=1.8x.01=1.8x10-2

  28. Scientific Notation Representation of a number in the form A x 10n

  29. Scientific Notation Computation Rules: Addition and Subtraction: 1.make the exponents match 2.add or subtract the coefficients 3.keep the exponent the same for the answer 4.correct the S.N. if it is not in the correct format 2x103+3x103 = 1.5x103+ 2.6x104 =

  30. Scientific Notation Computation Rules: Multiplication and Division: 1. multiply or divide the coefficients 2. add the exponents (for multiplication) or subtract the exponents (for division) 3. correct the S.N. if it is not in correct format 1x102 1.7x103 7.3x10-4/ 4.2x102 = X 1.2x105 X 2.3x10-1

  31. Tools of Measurement • Measuring Length • Ruler • Using the METRIC side • Record all certain digits PLUS one uncertain (record to the hundredths place) • Units: cm, mm, m, km

  32. Measuring Mass • Triple beam balance • Uses three (sometimes 4) beams to measure the mass of an object • Place solid object directly on pan • Place powders on filter paper or liquids in a container; deduct mass of the paper or container from the final measurement • Start with riders at largest mass and work back until the pointer reaches zero • Record all certain (up to hundredths) plus one uncertain (thousandths)

  33. Measuring Volume • Solids - Ruler • Volume = length x width x height • Units: cubic centimeter = cm3 • Liquids – Graduated Cylinder • Read the volume at the bottom of the meniscus • Be sure to place the graduated cylinder on a flat surface and look straight at the meniscus • Caution: Be sure to determine the increments on the graduated cylinder • Record all certain (usually tenths) plus one uncertain (usually hundredths) • Units: generally ml

  34. Unusually Shaped Objects – Water Displacement • Determine the volume of a filled graduated cylinder • Place the object in the graduated cylinder • Determine the volume of the graduated cylinder with the object • Subtract the volume to determine the amount of water displaced  the volume of the solid

  35. Measuring Temperature • Thermometer • Read the level of alcohol in the tube to determine the temperature • Caution: When reading negative temperatures be sure that you are reading in the correct direction • Units: degrees Celsius 25 (F) 25 (C) Temperature (C) 30 is hot 20 is nice 10 is chilly 0 is ice

  36. The Metric System: Conversions(APPROXIMATE)

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