LAB1 : SIGNIFICANT FIGURES

• Accuracy- signifies how close it comes to the standard value –

  that is, how nearly correct it is.
• Precision- refers to the agreement among repeated

  measurements – that is, the spread of the measurement or how close they are together.
• The more precise a group of measurements, the close together they are.
• Significant figures or significant digits- used to report a value, measured or calculated, to the correct number of decimal places or digits that will appear the precision of a value.
• The number of significant figures depends on how it is measured, or how it is calculated.
• The precision of a measurement is dependent on the equipment used to take it.
• Only one estimated value can ever be included in a measured quantity.
• Addition and Subtraction - When adding or subtracting numbers, find the to the fewest decimal places, then round the result to that number which is known decimal place.

  Illustrations: 5.623 g + 2.03 g – 1.5 g = 6.2 g
• Multiplication and Division - When multiplying or dividing numbers, find the number with the fewest significant figures, then round the result to that many significant figures.

  Illustrations: 6.4859 m/s x 0.26 m/s = 1.7 m/s
• Percent Error- The accepted or standard value of such a quantity found in textbooks and physics handbooks is the most accurate value obtained through sophisticated experiments or mathematical methods.
• The absolute difference between the experimental value and the accepted or standard value , written, is the positive difference in the values.
• The fractional error is the ratio of the absolute difference and standard value.
• The fractional error is commonly expressed as a percentage to give the percent error of experimental value.
• Percentage difference- is calculated when two experimental values, E1 and E2, are compared to each other, and there is no standard value for comparison.
• RULE NO. 2- Non-zero digits are significant.

  EX. 24.7 kg have 3 significant figures
• RULE NO. 1 - Values which are either exact numbers or numbers with perfect certainty contain an infinite number of significant figures.

  EX. 100 cm in one meter, number of trials, and Numbers two (2) and pi in the expression for the circumference of the circle.
• RULE NO. 3- Zeroes between non-zero digits are significant.

  EX. 90,057 m have 5 significant figures.
• RULE NO. 4- Zeroes to the right of a decimal point and to the right of a non-zero digit are significant.

  EX. 7.0 km have 2 significant figures, 3.00 x 108 m have 3 significant figures
• RULE NO. 5- Zeroes to the left of an expressed decimal point and to the right of a non-zero digit are significant.

  EX. 70,000.0 s have 6 significant figures
• RULE NO. 6- Zeroes to the right of the decimal point and to the left of a non-zero digit are not significant.

  EX. 0.00045 m have 2 significant figures
• RULE NO. 7- Zeroes to the right of a non-zero digit but to the left of an understood decimal point are not significant.

  EX. 928,000 cm have 3 significant figures
• Rules 6 and 7 can be expressed in scientific notation, using only

  significant figures in the number placed in the argument

  (before the power of 10).

  EX. (RULE 6) 0.00045 m ( 4.5 x 10-4 m ) 2 significant figures

  (RULE 7) 928,000 cm (9.28 x 105 cm) 3 significant figures
• Numerical Error- difference between the experimental value and the

  standard value.
• Percentage Error– refers to the fractional part in 100 that a measured

  value differs from the expected value.
• Percentage Error = [Experimental Value - Standard Value] / [Standard Value] x 100
• Percentage Difference= |xi-x| / x * 100 = |di| / x * 100
• NOT ACCURATE AND NOT PRECISE

  
• PRECISE BUT NOT ACCURATE

  
• ACCURATE BUT NOT PRECISE

  
• ACCURATE AND PRECISE