Measurements in Experiments The Science of Physics Measurements in Experiments

Numbers as Measurements To be of value, a measurement must have two parts in addition to the number Dimension – what kind of quantity Length, mass, time Unit – how much of the quantity Meter, kilogram, second

SI System Le Système International d’Unitès Used worldwide in science Seven base units, each describing a single dimension Units combine to form a derived unit Liter, Newton, Joule, o Celcius

SI System Length – meter Amount of substance – mole Mass – kilogram Electric current – Ampere Time – second Luminous intensity – candela Temperature – Kelvin

SI Prefixes Used to accommodate extremes Very large and small numbers Can also use scientific notation

SI Prefixes Kilo As you move down the Hecta stairs, move the decimal Deka right base units As you move deci up the stairs, centi move the decimal left milli

SI System Both dimension and unit must agree Length is in meters, not in kilograms When doing calculations with one dimension Prefixes must be the same Area=length*width m*m not m*cm 25m*10m not 25m*1000cm

Accuracy and Precision Accuracy – describes how close a measured value is to the true value of the quantity measured Precision – refers to the degree of exactness with which a measurement is made and stated How many decimal places there are Do all of the measurements agree with one another

Significant Figures Use significant figures to keep track of imprecision Significant figures – those digits in a measurement that are known with certainty plus the first digit that is uncertain When the last digit in a measurement is zero, it is difficult to tell if the zero is significant or not You can use scientific notation to show that a zero is significant

Significant Figures Rules for Significant Figures All non-zero digits are significant. (1-9) Zeroes between significant digits are significant. (101, zero is significant) Zeroes behind the decimal are significant if there is a non-zero number in front of them. (3.40, zero is significant)

Significant Figures Rules for Significant Figures If there is a decimal point, zeroes at the end of a number are significant. (50. zero is significant) Zeroes at the beginning of a number are not significant. (0.003, zeroes are not significant) If there is no decimal point, zeroes at the end of a number are not significant. (60, zero is not significant)

Rules for Calculating With Significant Figures Addition and Subtraction – answer should have same number of decimal places as the least amount of decimal places in the measurement Multiplication and Division – answer should have the same number of significant figures as the measurement with the least amount of significant figures

Rules for Rounding Round down – 0-4 Round up – 6-9 Special Rules for 5 Round to the nearest even number if nothing follows the five (32.25 ≈ 32.2 or 54.75 ≈ 54.8) Round up if there are digits following the 5 (54.7511 ≈ 54.8)

Error Analysis Some error always exists in any measurement Skill of the measurer and the precision of the instruments effect measurements When reading an instrument, always estimate one more place than you are given Multiple measurements minimizes the effects of experimental error

Error Analysis Mean – average Mean = (sum of values) / (number of values) Median – the value in the middle of the data when the data points are arranged in ascending order Mode – the most common data point Standard deviation – how far the data points vary with respect to the mean Normal distribution – a typically bell shaped curve when the data is graphed where most data falls within one or two standard deviations of the mean Outliers – any data points not within two standard deviations of the mean

Error Analysis Percent Error – used to compare an individual or average experimental value to the correct or accepted value Calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value and multiplying by 100%

Error Analysis Percent error is positive if the accepted value is greater than the experimental value Percent error is negative if the accepted value is less than the experimental value Percent Error = (Experimental Value – Accepted Value) / Accepted Value * 100%