Uncertainty in Measurement

Accuracy & Precision Accuracy- describes how well the results of a measurement agree with an accepted value Precision- the degree of exactness of a measurement, depends on the instrument used for measurement

Accuracy & Precision

Calculated to evaluate the ACCURACY of your experimental data: % Error Calculated to evaluate the ACCURACY of your experimental data: % Error = Accepted – Experimental x 100 Accepted  

Example: A book’s actual weight (accepted value) is 74.5 grams. You weigh the book and get 72.0 grams (experimental value). 74.5 g – 72.0 g x 100 = 3.35 % error 74.5 g The lower your percent error, the more accurate your results!

Scientific Notation A short way to express extremely large or small numbers Expressed as the product of a number between 1 and 10 and a whole number power of 10.

For large numbers: Move decimal to the left so that only ONE number is on the left of the decimal. However many spaces you moved the decimal is the exponent of 10 Example: 28,000,000 = 2.8 x 107

For small numbers beginning in zero: Move decimal to the right so that only ONE number is on the left of the decimal. However many spaces you moved the decimal is the NEGATIVE exponent of 10. Example: 0.00000064 = 6.4 x 10 -7

Significant Digits in Measurements There are five rules or guidelines that should be applied in determining whether a digit in a measurement is significant.

Rule #1 Every nonzero digit in a measurement is always significant. Example: 24.7 m 3 significant digits 715.55 g 5 significant digits

Rule #2 Zeros appearing between nonzero digits are significant. Example: 7003 m 4 significant digits 1.503 g 40.079 g 5 significant digits

Rule #3 Leading zeros are never significant. They serve as placeholders only. Example: 0.0071 m 2 significant digits 0.421 m 3 significant digits 0.000 099 m

Rule #4 Trailing zeros are only significant if the decimal point is written. Example: 70 m 1 significant digit 70.0 m 3 significant digits 27, 000 cm 2 significant digits

Rule #5 Counting numbers and exactly defined quantities have an unlimited number of significant digits. Example: 20 books ∞ number 1 hour = 60 minutes

Review How many significant digits are in each of the following measurements? a. 123 m b. 0.123 m c. 40.506 m d. 98 00.0 m e. 22 metersticks f. 30 m g. 0.07080 m h. 98 000 m

Significant Figures in Calculations Calculated values must be rounded so that they are consistent with the measurements from which they were calculated.

Multiplication and Division In calculations involving multiplication and division, answers should be rounded so that they contain the same number of significant digits as the measurement with the least number of significant digits. Example: 7.55 m x 0.34 m = 2.4526 m / 8.4 m =

Addition and Subtraction The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. Example: 12.52 m + 349.0 m + 8.24 m = 74.626 m – 28.34 m =

Review Measure and calculate the length of the perimeter of your note card. Round your answer to the correct number of significant digits. Measure and calculate the area of your note card (length x width). Round your answer to the correct number of significant digits. Calculate the number of minutes spent in school in a 5 day week.

Quiz: Significant Digits

Write the following number in correct scientific notation. How many significant digits are in each of the measurements below: 1) 100 m 2) 0.0230 m/s 3) 100.1 m 4) 2.0 x 1011 m/s 5) 50 metersticks 6) 10.380 s Solve the following problems and round to the correct number of significant digits. 7) 3.42 cm + 8.13 cm 8) 0.00457 cm x 0.18 cm 9) 85.0869 m2 ÷ 9.0049 m 10) 13.80 cm – 6.0741 cm Write the following number in correct scientific notation. 11) 0.00010500 µm