ch. 1 - measurement i. units of measurement. scientific method
TRANSCRIPT
CH. 1 - MEASUREMENT
I. Units of Measurement
Scientific Method
A. Derived Units Combination of base units.
Volume (mL or cm3) Formulas for volume of
sphere and cylinder
D = mV
1 cm3 = 1 mL1 dm3 = 1 L
Density (g/mL or g/cm3) mass per volume
B. Density
Density of a substance determines whether that substance will float or sink in a liquid
Density of a substance does not change
LiquidsMaterial Density (gm cm-3)
Water at 4 C 1.0000
Water at 20 C 0.998
Gasoline 0.70
Mercury 13.6
Milk 1.03
SolidsMaterial Density (gm cm-3)
Magnesium 1.7
Aluminum 2.7
Copper 8.3-9.0
Gold 19.3
Iron 7.8
Lead 11.3
Platinum 21.4
Uranium 18.7
Osmium 22.5
Ice at 0 C 0.92
B. DensityM
ass
(g)
Volume (cm3)
Δx
Δyslope D
V
m
B. Density Direct Proportion
Inverse Proportion
y
x
y
x
C. Measurement
Measurement is uncertain because
1. Instruments may have errors
2. Involves estimation
Measurement =
all certain digits + 1 uncertain digit
(estimate)
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
D. Percent Error
Indicates accuracy of a measurement
100literature
literaturealexperimenterror %
your value(observed value) accepted value
D. Percent ErrorA 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.
100g/mL 1.36
g/mL 1.36g/mL 1.40error %
% error = 2.9 %
E. 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
Sig Fig Rules
1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 2) ALL zeroes between non-zero numbers are ALWAYS significant. 3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant.(Helpful way to check rules 3 and 4 is to write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant.)
Sig Fig Examples
Number # Significant Figures Rule(s)
48,923 5 1
3.967 4 1
900.06 5 1,2,4
0.0004 (= 4 E-4) 1 1,4
8.1000 5 1,3
501.040 6 1,2,3,4
3,000,000 (= 3 E+6) 1 1
10.0 (= 1.00 E+1) 3 1,3,4
E. Significant Figures Counting Sig Figs
Count all numbers EXCEPT: Leading zeros -- 0.0025
what about:60.0025
Trailing zeros without a decimal point -- 2,500
what about: 2500.0
4. 0.080
3. 5,280
2. 402
1. 23.50
E. 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
E. 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
E. 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
20.0685+ 4.25 24.3185 ??
F. 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
F. Scientific Notation
1. 2,400,000 g
2. 0.00256 kg
3. 7 10-5 km
4. 6.2 104
mm
Practice Problems
2.4 106 g
2.56 10-3 kg
0.00007 km
62,000 mm