1. scientific notation and significant figures

2. In chemistry there are very big numbers
mole = 602,214,129,000,000,000,000,000.

3. In chemistry there are very big numbers
mole = 602,214,129,000,000,000,000,000.
18 grams/mole =
602,214,129,000,000,000,000,000 molecules
18 grams
and very small numbers

4. Scientific notation for large numbers
109 = 1 billion 1,000,000,000
106 = 1 million 1,000,000
103 = 1 thousand 1,000
102 = 1 hundred 100
101 = ten
100 =

5. Scientific notation for small numbers
10-9 = 1 billionth 1/1,000,000,000
10-6 = 1 millionth 1/1,000,000
10-3 = 1 thousandth 1/1,000
10-2 = 1 hundredtn 1/100
10-1 = 1 tenth 1/10
10-0 = /1

6. Exponents
7 is the exponent.
107
the exponent also called
the order of magnitude is
the most important part
of a number.
When numbers are multplied exponents are added.
1,000 x 100,000 =100,000,000
103 x = 108
1,000,000 x 1/100 = 10,000
106 x = 104

7. 106 x = ?
103 x 108 x 10-2 = ?
6 x 104 x 2 x = ?
If 1 x 103 = 1000 and 2 x 103 = 2000 what does 1.5 x 103 equal?
What does 15 x102 equal?
Does 1.5 x 103 = 15 x 102 = x 104 ?

8. Exponents
7 is the exponent.
107
When numbers are divided exponents are subtracted.
100,000 ÷ 1,000 = 100
105 ÷ = 102
10,000 ÷ (1/100) = 1,000,000
104 ÷ = 106

9. (103 x 106) ÷102 = ?
(8 x 103) ÷ (4 x 106) = ?
(20 x 104) ÷ (80 x 106) = ?
= 6 x 10?
60 = 6 ÷ 10?

10. (103 x 106) ÷ 10-2 = ?
8 x x 9 x 106 = ?
20 x 104 x 80 x 106 = ?
10? ÷ 102 = 104

11. 7.2 x 109 the exponent is 9. the digit 7 here
is the first significant figure.
the exponent
is 9.

12. 7.2 x 109 the exponent is 9. the digit 7 here
is the first significant figure
the exponent
is 9.
The most important part of a number is the exponent.
The second most important part of a number is its first
significant figure.

13. How many hours does it take to drive from NYC to Chicago?
Examples of questions which we can answer to one significant figure
How many hours does it take to drive from
NYC to Chicago?
How many generations ago did Jesus Christ
live?
How many shoes have you owned in your
lifetime?

14. How many hours does it take to drive from NYC to Chicago?
How many generations ago did Jesus Christ live?
60-80 generations
How many pairs of shoes have you owned in your lifetime?
30-60 pairs of shoes

15. In chem speak we say
How many hours does it take to drive from NYC to Chicago?
10 hours or 10 ± 2 hours
How many generations ago did Jesus Christ live?
70 generations or 70 ± 20 generations
How many pairs of shoes have you owned in your lifetime?
50 pairs or 50 ± 30 pairs of shoes

16. 7.2 (± 0.3) x 109 the exponent is 9. 0.3 is the error bar.
the digit 7 is the
first significant figure.
the exponent
is 9.
0.3 is the error bar.
The most important part of a number is the exponent.
The second most important part of a number is its first
significant figure.
The third most important part of a number is the error bar.

17. Significant figures
Significant figures is an approximate way in which scientists
communicate error bars.
84.3 means error bars are roughly between 0.9 to 0.09.
130 means error bars are roughly between 90 and 9.
Using significant figures, what is your life expectancy?
How tall are you?
How much money do you have in your checking account?

18. Error bars in graphs
78 years
s =15 years
Life Span
chart for
Americans
person
If unspecified, assume error bars indicate one standard deviation, s.
In most cases, 1 s marks where roughly 70% of the actual events occur.

19. Global warming error bars

20. To one significant figure what is a mole?

21. To one significant figure how many heart-
beats are there in a lifetime?

22. To one significant figure how many heartbeats are there in a lifetime?
To one significant figure 1 heartbeat every second.
1 minute
60 seconds
1 year
365 days
1 hour
60 minutes
1 day
24 hours
1 life
80 years x
≈ ?
1 hour
3600 seconds
1 year
365 days
1 day
24 hours
1 life
80 years x
≈ ?
1 hour
4000 seconds
1 year
400 days
1 day
20 hours
1 life
100 years x
≈ ?
1 hour
4 x 103 seconds
1 year
4 x 102 days
1 day
2 x 101 hours
1 life
1 x 102 years x
≈ 30 x 108=3 x 109
sec/life

23. The choo-choo train of unit conversion
1 hour
3600 seconds
1 year
365 days
1 day
24 hours
1 life
80 years x
≈ ?
1 hour
3600 seconds
1 year
365 days
1 day
24 hours
1 life
80 years x
≈ ?

24. even with the metric system, units get weird: the doctor's office
blood serum normal range
blood serum normal range
On a mole basis what is the most common metal ion
in blood?
To 1 significant figure, please convert the Na range to
mg/dL.
On a mole basis is there more creatinine or urea in blood?

25. Ion charge x Equivalents = 1 mole
this is
correct
Ion charge x Equivalents = 1 mole
1 mole Ca
2 Eq Ca

26. human blood serum units
normal range
normal range
Please convert the magnesium and
calcium normal ranges to a mmol/L
basis.
Please order the four main human
metallic blood electrolytes by molar
importance.

27. creatinine is a by-product of muscle degradation
C4H7N3O MW: g mol−1
Please calculate to one significant figure the upper end creatinine levels
for males in mg/dL .

28. estimation

29. As of July 2013, there are 6,930,000,000
people in the world.
To one significant figure how many people are there in the world?

30. The people of the world have united with a
How big is a mole?
The people of the world have united with a
new goal. We have decided to consume
one mole of M&Ms.
How many M&Ms would each of us have to
eat in each remaining second of our lives?

31. How big is the Earth?
Deducing answers from
knowledge we already know.

32. How big is the Earth? Deducing answers from knowledge we already know.
Always establish a strategy based on a number you know.

33. How big is the Earth? Deducing answers from knowledge we already know.
Always establish a strategy based on a number you know.
Find distance from Chicago to NYC. They are 1 hour apart. Mutiply
by 24 to get a trip round the world at latitude 40-45o. Estimate what
same trip at the Equator would be. Convert to kilometers.

34. How big is the Earth? 800 x 24 x 1.4 x 1.6 = 40,000 km
Deducing answers from
knowledge we already know.
Always establish a strategy based on a number you know.
Find distance from Chicago to NYC. They are 1 hour apart. Mutiply
by 24 to get a trip round the world at Latitude 40-45o. Estimate what
same trip at the Equator would be. Convert to kilometers.
800 x 24 x 1.4 x 1.6 =
40,000 km
google answer =40,075 km