Uncertainty in Measurement Accuracy Precision Accuracy describes how

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

Can you hit the bull's-eye? Three targets with three arrows each to shoot. How do they Both accurate and compare? precise Precise but not accurate Neither accurate nor precise

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

Example: A bead’s actual weight (accepted value) is 6 grams. You weigh the bead and get 3 grams (experimental value). 6 g – 3 g x 100 = 50 % error 6 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 = 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 n There are five rules or guidelines that should be applied in determining whether a digit in a measurement is significant.

Rule #1 n Every nonzero digit in a measurement is always significant. n Example: 24. 7 m 3 significant digits 715. 55 g 5 significant digits

Rule #2 n Zeros appearing between nonzero digits are significant. n Example: 7003 m 4 significant digits 1. 503 g 4 significant digits 40. 079 g 5 significant digits

Rule #3 n 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 2 significant digits n

Rule #4 n 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 n

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

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 n

Rounding Significant Digits n For THIS class, we will answer in 3 significant digits until we begin calculating with significant digits.