History of Measurement VFMS 2013 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 outstretched arms. 3. Span – distance from pinky to thumb on an outstretched hand. 4. Digit – length of one finger.

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.

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)

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

III. Fundamental Units of Measurement Quantity Unit Symbol Length meter m Mass gram g Volume liter l Time second s Force newton N Energy joule J

IV. Using the Metric System To convert to a larger unit, move the decimal point to the left or divide. To convert to a smaller unit, move the decimal point to the right or multiply. KING HENRY DECKED BULLIES DRINKING CHOCOLATE MILK Kilo Hecto Deka Base Unit deci centi milli K H D Volume: liter (l) Distance: Meter (m) Mass: gram (g) d c m 1000.0 100.0 10.0 1.0 0.1 0.01 0.001 Bigger Smaller

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

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)

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 )

Zeros used at the end or beginning are not significant 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)

Significant Figures Digits in a measured number that include all certain digits and a final digit with some uncertainty Number Number of Sig Figs 9.12 0.192 0.000912 9.00 9.1200 90.0 900. 900 3 5 ?

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

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.

In scientific notation, the number is separated into two parts 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

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.

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

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

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

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)

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

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

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

The Metric System: Conversions (APPROXIMATE)