PDF-ERROR AND SIGNIFICANT DIGITS

xTherelativeerrorisonlydenedforx0EXAMPLEIfx5andx51thentheerroris01theabsoluteerroris01andtherelativeerroris002Therelativeerrorisinvariantunderscaling1x x1103x 103x1001x 001xwhe. Measurements are always approximate. They depend on the precision of the measuring instrument – that is the amount of information that the instrument can provide.. Look at the graduations on a beaker versus the graduations on a graduated cylinder. Which instrument will provide better information?. Learning Goals …. … convert numbers to scientific notation. … convert measurements using the metric system. … identify the number of significant digits in a . measurement . Scientific Notation. Physical Science. What is a significant figure?. There are 2 kinds of numbers:. Exact: the amount of money in your account. Known with certainty.. What is a significant figure?. Approximate: weight, height—anything MEASURED. No measurement is perfect.. Objectives:. State the purpose of significant digits. State and apply the rules for counting and doing calculations with significant digits. One way engineers use significant digits….. What's so significant about significant digits?. &. Scientific Notation. Significant Figures. Scientist use significant figures to determine how precise a measurement is. Significant digits in a measurement include all of the known digits plus one estimated digit. Precision. Accuracy. Error Types. Significant Digits. Error Propagation. Error in Measurement.  . "Accuracy" means truth.. "Precision" means detail..  . Accuracy. Accurate: measured value very close to actual value.. Unit-1. Computer Arithmetic. 2140706 . – Numerical & Statistical Methods. Errors. An error is defined as the . difference. between the . actual value . and the . approximate value . obtained from the experimental . RULES FOR SIGNIFICANT DIGITS. 1. Non-zero digits are ALWAYS significant.. . Example-. 123456789. 2. Zeros that are between other significant digits are ALWAYS significant.. . Example. - 3004 . 3. Final zeros that occur before or after the decimal are ALWAYS significant.. Measuring with Precision. Defn: Those numbers that result from directly measuring an object. It shows the precision of the measurement.. Units must be included (no units no sd). The precision of the measurement depends upon the measuring instrument. 5700. 1. 2. 3. 4. Multiply. 843.5 * 21103. 17800380.5. 1.780 x 10. 8. 1.780 x 10. 7. 17800000. Which of the following instruments would give you the most accurate measurement?. Round to 3 significant digits.. The derailment on October 22, 1895 of the Granville-Paris Express that overran the buffer stop. The engine careened across almost 100 feet (30 meters) of the station concourse, crashed through a two-foot thick wall, shot across a terrace and sailed out of the station, plummeting onto the Place de Rennes 30 feet (10 meters) below where it stood on its nose. While all of the passengers on board the train survived, one woman on the street below was killed . errors. Numerical math != Math. . (cont.) . . Loss of significance. In Previous Lectures. :. Absolute and relative errors.. You. . considered and ran the code . numderivative.cc. ; . observed two types of errors – . 1 All non-zero digits are always significant154 3 sig figs 2 Interior zeros zeros between nonzero numbers are3 Leading zeros zeros at the beginning of a number are NOT 0103 3 sig figs 0000002 1 Diploma ExaminationsSignificant Digits measured values1For all non-logarithmic values regardless of decimal position any of the digits 1 to 9 is a significant digit 0 may be significant For example 12