1. Dimensional Analysis, Significant Figures, & the Metric System

2. Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT
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

3. Percent Error your value accepted value
Indicates accuracy of a measurement
your value
accepted value

4. Percent Error Example % error = 2.9 %
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 = 2.9 %

5. Significant Figures Indicates precision of a measurement.
Counting Sig Figs
Count all numbers EXCEPT:
Leading zeros
Trailing zeros without a decimal point -- 2,500

6. Counting Significant Figures
4 sig figs
3 sig figs
3. 5,280
3. 5,280
3 sig figs
2 sig figs

7. Calculating Significant Figures
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = g
4 SF
3 SF
3 SF
324 g

8. Calculating Significant Figures (cont’d.)
Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.
3.75 mL mL
7.85 mL
3.75 mL mL
7.85 mL
224 g
+ 130 g
354 g
224 g
+ 130 g
354 g
 7.9 mL
 350 g

9. 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 (“up”) Small # (<1)  negative exponent (“down”)
“If it was left up to me, I would put it right down”
Only include sig figs.

10. Scientific Notation Practice Problems
1. 2,400,000 g kg
3. 7  10-5 km
 104 mm
2.4  106 g
2.56  10-3 kg km
62,000 mm

11. Proportions
Direct Proportion
y = x y x
Inverse Proportion
y = 1 x y x

12. SI Units Quantity Symbol Base Unit Abbrev Length l meter m Mass m
kilogram kg
Time t
second s
Temp T
kelvin K
Amount n
mole
mol

13. SI Units Prefix Symbol Factor mega- M 106 kilo- k 103 BASE UNIT ---
100
deci- d
10-1
centi- c
10-2
milli- m
10-3
micro- 
10-6
nano- n
10-9
pico- p
10-12

14. M V D = Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L
Combination of base units
Volume (m3 or cm3)
length  length  length
1 cm3 = 1 mL
1 dm3 = 1 L
D = M V
Density (kg/m3 or g/cm3)
mass per volume

15. lecturePLUS Timberlake
Density
Density compares the mass of an object to its volume
D = mass = g or g
volume mL cm3
lecturePLUS Timberlake

16. Dimensional Analysis The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out

17. 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.

18. Dimensional Analysis Example
You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. lb
cm3
1.5 lb
1 kg
2.2 lb
1000 g
1 kg
1 cm3
19.3 g
= 35 cm3