Science and Measurement Chapter 1.4 The Foundations of Physical Science

Working With Measurements All measurements involve a degree of uncertainty How much error or uncertainty is acceptable? In the real world, it is IMPOSSIBLE to make measurement of the exact true value of anything (except counting)

Significant Digits Significant Digits or Significant Figures (or Sig Figs for short) are the meaningful digits in a measured quantity If you measure a paperclip and it is between 2.6 and 2.7. We usually say 2.65 cm But to a scientist 2.65 means between 2.62 and 2.67 The final digit in 2.65 is the 5, it represents the smallest amount and is always considered to be rounded up or down

Rules for Significant Digits Digits that are ALWAYS significant 1. Non-zero numbers Examples: 54982 = 5 2365149898=10 2. Zeros between two significant digits Examples: 93100008= 8 1001= 4 3. All final zeros to the right of a decimal point Examples: 4451.630= 7 5012677.26090= 12

Rules for Significant Digits Digits that are NEVER significant 1. Leading zeros to the right of a decimal point Examples: 0.002= 1 0.000456= 3 2. Final zeros in a number that does not have a decimal point Examples: 9900000= 2 8765210= 6

WANT A SHORT CUT???  This method depends on a question. When you are attempting to determine the number of sig fig’s in a number, ask yourself: Is the decimal point PRESENT or ABSENT?

Is the decimal point PRESENT or ABSENT? If the decimal point is NOT WRITTEN in the number, start on the RIGHT side of the number, go through any zero until you get to the first nonzero digit, underline it and all other numbers. The number of underlines is the number of sig fig’s! 300 = __1___ 2100 = __2___ 7890900 = __5___

Is the decimal point PRESENT or ABSENT? If the decimal point IS WRITTEN in the number, start on the LEFT side of the number, go through any zero until you get to the first nonzero digit, underline it and all other numbers. The number of underlines is the number of sig fig’s! 0.0033 = __2___ 0.000 000 4040 = __4___ 2.0000 = ___5__

Significant Figures Addition/Subtraction Rule For addition or subtraction, your answer should be rounded off to the LEAST number of decimal places in the problem.   325.471 + 77.210 402.681  Using the rule, this answer should be reported as 402 .68     1207.2 - 756.739 450.461  Using the rule, this answer should be reported as 450.5

Significant Figures Multiplication/Division Rule For multiplication and division problems, your answer should have the same number of sig. figs. as the LEAST number of sig. figs. in the problem. How many sig. figs.? 3  2 = 2 . 2.51 61 = __153.11_____ Final Answer _150___ How many sig. figs.? 2 / 3 = 2 . 450/32.1 = 14.0186915 Final Answer ___14___  

Accuracy, Precision, and Resolution Accuracy- how close a measurement is to an accepted or true value Precision- describes how close together or reproducible reproducible repeated measurements are Resolution- refers to the smallest interval that can be measured

Significant Differences In everyday conversation, “same” means two numbers that are the same exactly, like 2.56 and 2.56. When comparing scientific results “same” means “not significantly different”. Significant differences are differences that are MUCH larger than the estimated error in the results

Error and Significance How can you tell if two results are the same when both contain error (uncertainty)? When we estimate error in a data set, we will assume the average is the exact value. If the difference in the averages is at least three times larger than the average error, we say the difference is “significant”.

Error How you can you tell if two results are the same when both contain error. Calculate error Average error Compare average error