1. Unit 2 Measurements

2. World’s Roundest Object
Matter - anything that occupies space and has mass
mass – measure of the quantity of matter
SI unit of mass is the kilogram (kg)
1 kg = 1000 g = 1 x 103 g
La Grande K
1 Kg Pt/Ir alloy
World’s Roundest Object
weight – force that gravity exerts on an object
weight = mass  g (F = ma)
on earth, g = 1.0
on moon, g ~ 0.1
A 1 kg bar will weigh
1 kg on earth
0.1 kg on moon

3. International System of Units (SI) Base Units
Used in this class and should have memorized
All other units are derived from these units and are known as Derived Units
Velocity: m/s
Force: 1 Newton = 1 kg•m/s2
Volume: m3

4. Prefixes can be used to simplify for extremely large or small quantities of base units
“mu”
Used most often in this class, be sure to memorize.

5. Prefix examples Driving 321,000 meters to LR = 321 kilometers
Radio station 90.9 MHz = 90,900,000 Hz
A mosquito weighs 2.5 milligrams (mg) = grams (g)
A dust mite’s length meters = 200 micrometers (mm)

6. 1 Mm = 106 L 10-6 ML = 1 L 1km = 103 L 10-3 kL = 1 L Liter (base)
Conversion factors can be written/used 2 ways
1 Mm = 106 L
1km = 103 L
Liter (base)
1 cL = 10-2 L
1 mL = 10-3 L
1 mL = 10-6 L
1 nL = 10-9 L
10-6 ML = 1 L
10-3 kL = 1 L
Liter (base)
102 cL = 1 L
103 mL = 1 L
106 mL = 1 L
109 nL = 1 L Or
I favor the forms using (+) exponents

7. Volume – SI derived unit for volume is cubic meter (m3)
(cm3 is commonly used)
1 cm3 = 1 mL

8. Density – SI derived unit for density is kg/m3
1 g/cm3 = 1 g/mL = 1000 kg/m3
*more commonly used
density =
mass
volume
d = m V
2 L of Os
= 100 lbs

9. Example 1.1 Gold is a precious metal that is chemically unreactive.
It is used mainly in jewelry, dentistry, and electronic devices.
A piece of gold ingot with a mass of 301 g has a volume of
15.6 cm3. Calculate the density of gold.
gold ingots

10. Example
1.2
The density of mercury, the only metal that is a liquid at room temperature, is 13.6 g/mL. Calculate the mass of 5.50 mL of the liquid.
d = m V

11. Failed to convert English to metric units
Chemistry In Action
On 9/23/99, $125M Mars Climate Orbiter entered Mars’ atmosphere 100 km (62 miles) lower than planned and was destroyed by heat.
Failed to convert English to metric units
1 lb = 1 N
1 lb = 4.45 N
“This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

12. Scientific Notation The number of atoms in 12 g of carbon:
602,200,000,000,000,000,000,000
6.022 x 1023
The mass of a single carbon atom in grams:
1.99 x 10-23
We can factor out powers of 10 to simplify very large or small numbers
Exponent (n) is a positive or
negative integer
N is the base number
between 1 and 10
N x 10n

13. Scientific Notation . . Base x 10exponent Base number ≥ 1 and < 10
= 3.2 x Decimal moved left so (+)
= 7.4 x Decimal moved right so (–) .
320,000 .

14. Scientific Notation Practice
Write these in long notation
2.0 x 103
3.58 x 10-4
4.651 x 107
9.87 x 10-2
Write these in scientific notation
579
96,000
0.0140

15. Mathematics in Scientific Notation
Addition or Subtraction: Must have same exponent
Write each quantity with the same exponent n
Combine N1 and N2
The exponent, n, remains the same
4.31 x x 103 =
4.31 x x 104 =
4.70 x 104
Tip: change smaller number to match larger exponent
1.36 x 10-1 – 4 x 10-3 =
1.36 x 10-1 – 0.04 x 10-1 =
More practice:
1.45 x x 10600
= 1.32 x 10-1

16. Mathematics in Scientific Notation
Multiplication: Add exponents
(4.0 x 10-5) x (7.0 x 103) =
(4.0 x 7.0) x (10-5+3) =
28 x 10-2 =
2.8 x 10-1
Multiply N1 and N2
Add exponents n1 and n2
Practice: (3 x 10250) (7.2 x )
Division: Subtract exponents
8.5 x 104 ÷ 5.0 x 109 =
(8.5 ÷ 5.0) x =
1.7 x 10-5
Divide N1 and N2
Subtract exponents n1 and n2
Practice: 9.5 x 1045) ÷ (3.7 x 1050)

17. b) Rewrite above numbers using the nearest SI prefix
Bell Ringer
a) Write in scientific notation
8,705,000 m L
sec
9,300 g
b) Rewrite above numbers using the nearest SI prefix
c) Perform the below mathematics in Sci. Notation
(9.01 x 103 g) + (3.8 x 102 g)
(3.98 x 10-2 m) – (8.2 x 10-3 m)
(2.61 x 107 m) x (9.87 x 10-2 m)
(8.4 x 109 g) ÷ (2.0 x 104 mL)

18. e.g. mass of hydrogen atom:
Precision indicates to what degree we know our measurement. (Arithmetic precision)
A measurement of 18.0 grams could be made on an average countertop food scale (balance). (~$20)
A high-precision milligram scale could weigh the same sample with a much higher precision ( grams) (~$1,500)
Every measurement is limited by the equipment’s level of precision. (Never exact)
e.g. mass of hydrogen atom:
grams

19. Significant Figures: Used to prevent uncertainty from rounding of various measured quantities with various levels of precision.
1) Any digit that is not zero is significant
1.234 kg significant figures
34,000 mm 2 significant figures
2) Zeros between nonzero digits are significant
606 cm significant figures
50,050 s 4 significant figures
3) Zeros to the left of the first nonzero digit are not significant
0.08 mL significant figure
ML 2 significant figures
4) If a number is greater than 1, then all zeros to the right of the decimal point are significant
2.0 mg significant figures
g 5 significant figures
5) If a number is less than 1, then only the zeros at the end are significant
g 3 significant figures
g significant figures

20. Significant Figures 0.001400 m ____ 4 significant figures 500 mL __
Every significant figure is shown when using Scientific notation. m
____
4 significant figures
1.400 x 10-3 Not 1.4 x 10-3
500 mL __
2 significant figures
5.0 x 102 Not 5 x 102

21. Example 1.4 Unit Conversions 478 cm 0.0430 kg 600,001 g
Determine the number of significant figures in the following measurements:
478 cm kg
600,001 g
1.310 × 1022 atoms
0.85 m
7000 mL

22. Example
1.4 Solution
478 cm -- Three, because each digit is a nonzero digit.
(b) 600,001- Six, because zeros between nonzero digits are significant.
(c) m -- Three, because zeros to the left of the first nonzero digit do not count as significant figures.
(d) kg -- Three. The zero after the nonzero is significant because the number is less than 1.
(e) × 1022 atoms -- Four, because the number is greater than one so all the zeros written to the right of the decimal point count as significant figures.

23. Example
1.4 solution
7000 mL -- This is an ambiguous case. The number of significant figures may be four (7.000 × 103), three (7.00 × 103), two (7.0 × 103), or one (7 × 103).
This example illustrates why scientific notation must be used to show the proper number of significant figures.
If no decimal is present it is usually assumed only non-zeros are significant. If a decimal is present, than all zero’s are significant.
7,000 mL ≠ 7,000. mL
They display differing degrees of precision.

24. Significant Figures Addition or Subtraction ± 50 mL ± 1.0 mL
The answer cannot have more digits to the right of the decimal point than any of the original numbers.
Use the least precise number. L
1.1 +
90.492
± 50 mL XX
one significant figure after decimal point
round off to 90.5
± 1.0 mL
3.70
0.7867 XX
two significant figures after decimal point
round off to 0.79

25. Significant Figures 4.51 x 3.0006 = 13.532706 = 13.5
Multiplication or Division
The number of significant figures in the result is set by the original number that has the smallest number of significant figures.
4.51 x =
= 13.5
round to 3 sig figs
3 sig figs
6.8 ÷ =
= 0.061
2 sig figs
round to 2 sig figs

26. Example
1.5
Carry out the following arithmetic operations to the correct number of significant figures:
11,254.1 g g
66.59 L − L
8.16 m × kg
(d) kg ÷ 88.3 mL
(e) (2.64 × 103 cm) + (3.27 × 102 cm)

27. Example
1.5 Solution
Solution In addition and subtraction, the number of decimal places in the answer is determined by the number having the lowest number of decimal places.
(a)
(b)

28. Example
1.5 Solution
In multiplication and division, the significant number of the answer is determined by the number having the smallest number of significant figures.
(c)
(d)
(e) First we change 3.27 × 102 cm to × 103 cm and then carry out the addition (2.64 cm cm) × Following the procedure in (a), we find the answer is 2.97 × 103 cm.

29. Bell Ringer
a) Perform the below mathematics in Sci. Notation. using Significant Figures in your answer.
(9.8 x 105 g) + (6.75 x 104 g)
(5.98 x 10-6 m) – (7 x 10-8 m)
b) Rewrite the first 2 solutions
using the nearest SI prefix
3. (2.612 x 1010 m) x (9.87 x 10-3 m)
4. (7 x 102 mg) ÷ (1.875 x 104 mL)

30. Significant Figures Exact Numbers
Numbers from definitions or numbers of objects are considered to have an infinite number of significant figures.
The average of three measured lengths: 6.64, 6.68 and 6.70? 3
= = 7
= 6.673
Because 3 is an exact number, not a measured number; It is not used for sigfigs.
How many feet are in 6.82 yards?
6.82 yards x 3 ft/yard
= 20.5 ft = 20 ft
1 yard = exactly 3 ft by definition

31. Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise

32. Ex. I weigh a 3 kg block on three different scales:
Percent Error
A way to determine how accurate your measurements are to a known value.
|Obtained value – Actual value| x 100% Actual Value
Ranges between 0 and 100%
Ex. I weigh a 3 kg block on three different scales:
3.2 kg, 3.0 kg, 3.1 kg = 3.1 kg average
3.1 – 3.0
3.0
x 100% = 3.3% error

33. Dimensional Analysis of Solving Problems (Train-Tracks)
Determine which unit conversion factors are needed
Carry units through calculation
If all units cancel except for the desired unit(s), then the problem was solved correctly.
given quantity x conversion factor = desired quantity
desired unit
given unit
given unit x
= desired unit

34. Train Track Example How many inches are in 3.0 miles?
Identify beginning information
Draw a train track
Write measurement as a fraction
3 miles

35. Train Track Example How many inches are in 3.0 miles?
We are going from a larger measurement to a smaller one.
Find a conversion factor you know that changes miles into something smaller.
Conversion Factor: 1 mile = 5,280 feet
Write your conversion factor on the track so that miles cancels out and you are left with the unit feet.
3 miles
5280 feet
1 mile
Always need same units on opposite sides to cancel out

36. Again, place conversion factor so that the previous unit cancels out.
Train Track Example
How many inches are in 3.0 miles?
We now need another conversion factor between Feet and Inches: 1 foot = 12 inches
Again, place conversion factor so that the previous unit cancels out.
3.0 miles
5280 feet
1 mile
12 inches
1 foot

37. Inches are the only remaining unit ✔
Train Track Unit Conversions
How many inches are in 3.0 miles?
3.0 miles
5,280 feet
1 mile
12 inches
1 foot
Inches are the only remaining unit ✔
Multiply all numbers on the top
Divide all numbers on the bottom
3.0 x 5,280 x 12
1 x 1
= 190,080 inches
= 1.9 x 105 inches
(2 sig figs)
More practice:
Convert 1.40 x 10-6 g to mg

38. Example Metric to Metric Conversion Problems
Convert 2.79 x 105 mm to km
Don’t try to convert directly from mm to km. Go to the base unit (m) first
Conversion factors: 1,000 mm = 1 m; 1,000 m = 1 km
2.79 x 105 mm
1 m
103 mm
1 km
103 m
Kilometers are the only remaining units ✔
2.79 x 105
103 x 103
= 2.79 x 10(5-3-3)
= 2.79 x 10-1 km
(3 sig figs)
More practice:
Convert 3.4 x 103 cg to mg

39. Example
A person’s average daily intake of glucose (a form of sugar) is pound (lb). What is this mass in milligrams (mg)? (1 lb = g.)
A metric conversion is needed to convert grams to milligrams (1 mg = 1 × 10−3 g)
(Or we could write: 1,000 mg = 1 g)
Either Conversion factor will work
453.6 g
1 lb
103 mg
1 g lb
= 37, mg
= 3.78 x 104 mg
(3 sig figs)

40. Example 2-D Conversion Problems (Unit1/Unit2)
Convert 70.0 miles/hour to m/s
We convert one unit at a time, followed by the other
Conversion factors: 1 mile = 1,609 meters; 1 hour = 60 min; 1 min = 60 sec
*Note: to cancel out hours (on bottom) it must appear again on the top
70.0 miles
1 hour
1609 meter
1 mile
1 hour
60 min
1 min
60 sec
Meter/sec are the only remaining units ✔
70.0 x 1,609 x 1 x 1
1 x 1 x 60 x 60
= m/s
= 31.3 m/s
More practice:
Convert 3.4 kg/L to g/mL

41. 2-D Conversion Problems (Unit#)
Example
Convert 2.5 x 10-5 m3 to mm3
Conversion factors: 1 m = 1,000 mm
1 m3 ≠ 1,000 mm3
1. Write the 1-D units first (1m = 103m)
2. Add exponent to entire conversion factor
1 m3 = (1,000)3 mm3 ✔ 3
2.5 x 10-5 m3
1000 mm
1 m
2.5 x 10-5 m3
109 mm3
1 m3 =
2.5 x 10-5 x 109
= 2.5 x 104 mm3
More practice:
Convert 34 yd2 to ft2

42. 2-D Conversion Problems (Unit#)
Example
2-D Conversion Problems (Unit#)
Convert 6.70 x 103 ft2 to inches2
Conversion factors: 1 ft = 12 in
1 ft2 ≠ 12 in2
1. Write the 1-D units first (1ft = 12 in)
Alternate 2nd Method
2. Write the same conversion factor again until they cancel
1 ft2 = 122 in2✔
6.70 x 103 ft2
12 in.
1 ft
12 in.
1 ft
= x 105 in2
More practice:
Convert 34 yd3 to ft3

43. Example
An average adult has 5.2 L of blood. What is the volume of blood in m3?
1 mL = 1 cm3
1 cm3
1 mL
1 m3
1003 cm3
103 mL
1 L
5.2 L
= 5.2 x 10-3 m3

44. Example 1 hour 1 day 760 miles 24 hours = 1.4 days
2-D Conversion Problem
The circumference of the earth is approximately 2.49 x 104 miles long.
If the speed of sound travels at 760 mph, how many days would it take a sound wave to circulate Earth’s circumference.
Starting with length and velocity; needing time
Conversion factor: 760 miles = 1 hour
1 hour
760 miles
1 day
24 hours
2.49 x 104 miles
= 1.4 days

45. More Practice Conversion problems
Convert 3.0 mL to ounces (33.8 oz = 1 L)
1.67 Mm to mm
2.35 x 1012 inches to cm (1 ft = m)
3.50 x 104 mL to cL
42.0 km/h to ft/ms
0.55 Acres to m2 (247 acre = 1 km2)
10.6 g/mm3 to kg/m3
Review
Unit Conversion & Significant Figures: Crash Course Chemistry #2

46. Sample of Topics to Study
Metric base units
Derived unit
Using Prefixes
Significant Figures (+ math)
Scientific Notation (+ math)
% Error calculation
Accuracy
Precision
Dimensional Analysis