The Foundations of Physical Science
All measurements involve a degree of uncertainty How much acceptable?
error or uncertainty is In the real world, it is IMPOSSIBLE make measurement of the exact true value of anything (except counting) to
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 and 2.67
between 2.62 The final digit in 2.65 is the 5, it represents the smallest amount and is always considered to be rounded up or down
Digits that are ALWAYS 1. Non-zero numbers Examples: 54982 = 5 significant 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
Digits that are NEVER significant 1. Leading point zeros to the right of a decimal 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
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 ABSENT ?
If the decimal point is NOT WRITTEN in the number, start on the other numbers. RIGHT side of the number, go through any zero until you get to the first nonzero digit, underline it and all 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 number of sig fig’s! 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
0.0033 = __ 2 ___ 0.000 000 4040 = __ 4 ___ 2.0000 = ___ 5 __
For addition or subtraction, your answer should be rounded off to the LEAST number of decimal places in the problem.
402.681 as 402 .68
Using the rule, this answer should be reported 1207.2
450.461 as 450.5 Using the rule, this answer should be reported
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.? 2.51
3 2 = 2 .
61 = __ 153.11
_____ Final Answer _ 150 ___ How many sig. figs.? 2 450/32.1 = 14.0186915
/ 3 = 2 .
Final Answer ___ 14 ___
Accuracy- how close a measurement is to an accepted or true value Precision- describes how measurements are close together or reproducible reproducible repeated Resolution- refers to the smallest interval that can be measured
In everyday conversation, “ like 2.56 and 2.56.
same ” means two numbers that are the same exactly, When comparing scientific results “same” means “ not significantly different ”.
that are MUCH error in the results are differences larger than the estimated
How can you tell if two results are the same when both contain
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 “
How you can you tell if two results are the same when both contain error.
Calculate error Average error Compare average error