Measurement in Science
CHE100
Graham/09
Associated Reading: Stoker(textbook), chapter 2
Two ways to Measure :
Qualitative –
Quantitative -
The most common quantities
to be measured:
All Measurements include 3 features
Uncertainty in Measurement
Accuracy –
Precision –
Error A.)
Systematic Errors
B.)
Random Errors
1.) ______________________
2.) ______________________
3.) ______________________
Pg. 2
Significant Figures –
“Sig Figs”
The digits in any _______________________ that are known with
certainty plus _____________________ that is uncertain.
Rule 1 – Digits 1 – 9 (All non-zero digits) Always Significant
examples:
Rule 2 – Leading Zeros (zeros preceding non-zero digits)
Not Significant. They indicate position of decimal point
examples:
Rule 3 – Confined zeros (zeros between non-zeros) Always Significant
examples:
Rule 4 - Trailing zeros (at end of a number)
- if decimal point is present in number trailing zeros are Significant.
- otherwise, trailing zeros are not Significant
examples:
________________________________________________________________________
Rules for Rounding
1.)
If the 1st digit dropped is less than 5, leave the digit before it unchanged.
example:
2.)
If the 1st digit dropped is greater than or equal to 5, increase the digit
before it by 1.
example:
3.)
432.13 (rounded to 4 sf) __________
432.17 (rounded to 4 sf)  _________
Note: We are not following
the “Even-Odd” rule as
described in the text, pg. 25
When digits to the left of the decimal are to be dropped,
they are replaced by zeroes.
The Magnitude of the number must never be changed by rounding.
examples: 432,117 (rounded to 3 sf) = ______________
432,153 (rounded to 4 sf ) = ______________
4.)
In multi-step calculations – it is best to keep additional sf through the
calculations, and then round the final answer.
5.)
Rounding is not a sequential process
example: 1.324999 rounded to 3 s.f. is 1.32 (Not 1.33)
Pg. 3
There are two kinds of numbers:
Inexact Numbers – are obtained from ________________________, and thus contain a
degree of uncertainty
Exact Numbers have _______________________ or are integers resulting from
counting numbers or objects
These numbers have __________________________ (They are known exactly)
And therefore, have______________________ Significant Figures.
a.) Definitions:
b.) Counted items:
c.) Simple fractions:
Measured quantities Always have a degree of uncertainty
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Significant Figures and Calculations
In any mathematical operation, the answer cannot reflect more precision than the
___________________________ quantity in the calculation.
Multiplication and Division
(least precise = fewest sig. figs)
Result must be reported with the same number of Sig. Figs.
as the ______________________________________________________
example 1:
3.0123 x 0.002356 x 9.01
=
____________________ (calc. ans.)
rounds to ___________________
________________________________________________________________________
example 2:
0.8345
1.1
= ___________________(calc. ans.)
rounds to ________________
Pg. 4
example 3:
100.58 x 50.1
0.28
=
_________________ (calc. ans.)
rounds to ______________
result is best expressed in Scientific Notation. _______________
________________________________________________________________________
Multiplication and Division and Scientific Notation
example 1: 2.36 x 103 x 1.134 x 105 = _____________________
___________________________________________________________________
example 2: 5.83 x 10-6
x
3.4256 x 104
= _______________________
___________________________________________________________________
example 3:
5.8321 x 104
2.331 x 10-3
=
_________________________
________________________________________________________________________________________________
Sometimes the calculator displays too few sig. figs (when they are zeros).
Be prepared to add significant zeros to calculator results.
example 4:
8.00
2.00
= _____ (calc. ans)
______ (correct answer)
Pg. 5
Addition and Subtraction
The final answer will have the same number of ___________ as the measurement with
the ________________ decimal places.
Result cannot have more digits to the right of the decimal point than any of the original numbers.
(Notice – we don’t count sig. figs, we count decimal places)
example1:
5.62 + 0.0223 + 9.831 = ____________
Round to
(calc. ans.)
___________
________________________________________________________________________
example 2:
1632.1 - 58.2345 = __________ (calc. ans.)
round to
__________
________________________________________________________________________
How is the weak link identified if there is no decimal in the number?
The measurement whose last sig. fig is furthest to the left defines the weak link.
example 3: 11,320
+ 1200 + 12 =
____________ (calc. ans.)
round to __________
The weak link is the measurement with the _______________________________
In this problem, the answer can only be expressed with certainty to the ________________