Transcript Ch. 3 Scientific Measurements

Chapter 3
Scientific
Measurement
I
II
III
Measurements
Qualitative Quantitative
 Gives results
in a
description,
nonumerical
form
 Give results in
a definite
form, usually
numbers and
units
Accuracy vs. Precision
 Accuracy - how close a measurement is
to the accepted value
 Precision - how close a series of
measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
Accuracy vs. Precision
Percent Error
 Indicates accuracy of a measurement
% error 
experimental  literature
literature
your value
accepted value
 100
Percent Error
 A student determines the density of a
substance to be 1.40 g/mL. Find the % error if
the accepted value of the density is 1.36 g/mL.
% error 
1.40 g/mL  1.36 g/mL
1.36 g/mL
% error = 2.9 %
 100
Percent Error
 A technician experimentally
determined the boiling point of octane
to be 124.1ºC. The actual boiling point
of octane is 125.7ºC. Calculate the
error and percent error.
Error= 1.6ºC
Percent error= 1.273 %
Significant Figures
 Indicates precision of a measurement.
 Recording Sig Figs
 Sig figs in a measurement include the
known digits plus a final estimated digit
2.31 cm
Significant Figures
 Counting Sig Figs

All non-zero numbers are sig figs
 Zeros depend on location in number:



LEADING zeros never count --------0.0025
EMBEDDED zeros always count---10,005
TRAILING zeros only count if
there is a point. --------------2,500 2,500.
Significant Figures
Counting Sig Fig Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
Rounding
 Need to use rounding to write a
calculation correctly
 Calculator gives you lots of
insignificant figures and you must
round to the right place
 When rounding, look at the digit after
the one you can keep
Greater than or equal to 5, round up
Less than 5, keep the same
Rounding
 Round each measurement to 3 sig






figs.
A. 87.073 meters 87.1meters
B. 4.3621 meters 4.36 meters
C. 0.01552 meter 0.0155 meter
9010 meters
D. 9009 meters
E. 1.7777 meters
1.78 meters
F. 629.55 meters
630 meters
Scientific Notation
 Round each measurement to the




number of significant figure shown in
parenthesis. Write the answers in
scientific notation.
2
3.147
X
10
A. 314.721 meters (4)
B. 0.001775 meter (2)
1.8 108
C. 64.32 X 10-1 meters (1) 60 X 10-1
D. 8792 meters (2)
8.8 X 103
Significant Figures
 Calculating with Sig Figs (con’t)
 Add/Subtract - The # with the lowest
decimal value determines the place of
the last sig fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL  7.9 mL
224 g
+ 130 g
354 g

350g
Significant Figures
 C. 8.7 g + 15.43 g + 19 g = 43.13 g
 D. 853.2 L – 627.443 L = 225.757 L
 E. 5.47 m + 11m + 87.3000 m =
103.770m
C. 8.7
D. 853.2
15.43
- 627.443
+ 19
225.757
43.13 43
225.8
E. 5.47
11
+ 87.3000
103.770
104
Significant Figures
 Calculating with Sig Figs (con’t)
 Exact Numbers do not limit the # of sig
figs in the answer. UNLIMITED SIG FIGS
 Counting
 Exact
 “1”
numbers: 12 students
conversions: 1 m = 100 cm
in any conversion: 1 in = 2.54 cm
Significant Figures
 Calculating with Sig Figs
 Multiply/Divide - The # with the fewest
sig figs determines the # of sig figs in
the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
Significant Figures
Practice Problems
1. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2 SF
a. 67 X 55 = 3685  3700
d.
0.034 X 8.8 = 0.2992  0.30
Scientific Notation
65,000 kg  6.5 × 104 kg
 Converting into Sci. Notation:
 Move decimal until there’s 1 digit to its
left. Places moved = exponent.
 Large # (>1)  positive exponent
Small # (<1)  negative exponent
 Only include sig figs.
Scientific Notation
Practice Problems
7. 2,400,000 g
2.4 
8. 0.00256 kg
2.56 
9. 7  10-5 km
0.00007 km
10. 6.2  104 mm
62,000 mm
6
10
g
-3
10
kg
Scientific Notation
 Convert between scientific notation





and regular notation *without
changing the # of sig figs*
A. 4.61 X 10-4
B. 3.69 X 106
C. 0.000597
D. 23,000,000
E. 8.00 X 102
Scientific Notation
 Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
(5.44 X10 EE
7)
÷
(8.1X10 EE
4) ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol