I II III I. Using Measurements CH. 2 - MEASUREMENT
Dec 29, 2015
I
II
III
I. Using Measurements
CH. 2 - MEASUREMENT
A. 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
C. Significant Figures
Indicate precision of a measurement.
Recording Sig Figs
Sig figs in a measurement include the known digits plus a final estimated digit
2.32 cm
C. Significant Figures
Counting Sig Figs
Count all numbers EXCEPT:
Leading zeros -- 0.0025
Trailing zeros without a decimal point -- 2,500
USA??
4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
4 sig figs
3 sig figs
3 sig figs
2 sig figs
C. 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
324 g
4 SF 3 SF3 SF
C. 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
3.75 mL
+ 4.1 mL
7.85 mL
C. Significant Figures
Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm
C. Significant Figures
5. (15.30 g) ÷ (6.4 mL)
Practice Problems
= 2.390625 g/mL
18.1 g
6. 18.9 g
7. - 0.84 g18.06 g
4 SF 2 SF
2.4 g/mL2 SF
D. Scientific Notation
Converting into Sci. Notation:
Move decimal until there’s 1 digit to its left. Places moved = exponent.
Large # (>1) positive exponentSmall # (<1) negative exponent
Only include sig figs.
65,000 kg 6.5 × 104 kg
D. Scientific Notation
7. 2,400,000 g
8. 0.00256 kg
9.7 10-5 km
10. 6.2 104 mm
Practice Problems
2.4 106 g
2.56 10-3 kg
0.00007 km
62,000 mm
D. Scientific Notation
Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
5.44EXPEXP
EEEE÷÷
EXPEXP
EEEE ENTERENTER
EXEEXE7 8.1 4
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Type on your calculator:
E. SI Units
Quantity Base Unit Abbrev.
Length
Mass
Time
Temp
meter
kilogram
second
kelvin
m
kg
s
K
Amount mole mol
Symbol
l
m
t
T
n
F. Derived Units
Combination of base units.
Volume (m3 or cm3) length length length
D = MV
1 cm3 = 1 mL1 dm3 = 1 L
Density (kg/m3 or g/cm3)mass per volume
Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
Density
An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ?
WORK:
M = DV
M = (13.6 g/cm3)(825cm3)
M = 11,200 g
V
MD
Density
A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V = ?
M = 25 g
WORK:
V = M D
V = 25 g
0.87 g/mL
V = 29 mLV
MD
SI Prefix Conversions
mega- M 106
deci- d 10-1
centi- c 10-2
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
nano- n 10-9
pico- p 10-12
kilo- k 103
mo
ve le
ft
mo
ve r
igh
t BASE UNIT --- 100
SI Unit Conversions
King Henry Died__drinking chocolate milk
K H D __ d C M
=
SI Prefix Conversions
NUMBERUNIT
NUMBER
UNIT
532 m = _______ km0.532
SI Prefix Conversions
1) 20 cm = ______________ m
2) 0.032 L = ______________ mL
3) 45 m = ____ mm
4) 805 dm = ______________ km
0.2
0.0805
45,000
32
Dimensional Analysis
Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.
Dimensional Analysis
Lining up conversion factors:
1 in = 2.54 cm
2.54 cm 2.54 cm
1 in = 2.54 cm
1 in 1 in
= 1
1 =
Dimensional Analysis
How many milliliters are in 1.00 quart of milk? (1L = 1.057 qt)
1.00 qt 1 L
1.057 qt= 946 mL
qt mL
1000 mL
1 L
Dimensional Analysis
You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. (1 kg = 2.2 lbs)
lb cm3
1.5 lb 1 kg
2.2 lb= 35 cm3
1000 g
1 kg
1 cm3
19.3 g
Dimensional Analysis
5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm)
8.0 cm 1 in
2.54 cm= 3.2 in
cm in