scientific notation and significant figures

mole = 602,214,129,000,000,000,000,000.

In chemistry there are very big numbers

mole = 602,214,129,000,000,000,000,000.

In chemistry there are very big numbers

18 grams/mole = 602,214,129,000,000,000,000,000 molecules

18 grams

and very small numbers

Scientific notation for large numbers

109 = 1 billion 1,000,000,000106 = 1 million 1,000,000103 = 1 thousand 1,000102 = 1 hundred 100 101 = ten 10100 = 1 1

Scientific notation for small numbers

10-9 = 1 billionth 1/1,000,000,00010-6 = 1 millionth 1/1,000,00010-3 = 1 thousandth 1/1,00010-2 = 1 hundredtn 1/100 10-1 = 1 tenth 1/1010-0 = 1 1/1

1,000 x 100,000 =100,000,000103 x 105 = 108

1,000,000 x 1/100 = 10,000106 x 10-2 = 104

107

7 is the exponent.

When numbers are multplied exponents are added.

Exponentsthe exponent also called the order of magnitude is the most important part of a number.

106 x 105

= ?103 x 108 x 10-2

= ?6 x 104 x 2 x 10-1

= ? 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 = 0.15 x 104 ?

100,000 ÷ 1,000 = 100105 ÷ 103 = 102

10,000 ÷(1/100) = 1,000,000104 ÷ 10-2 = 106

107

7 is the exponent.Exponents

When numbers are divided exponents are subtracted.

(103 x 106) ÷102 = ?

(8 x 103) ÷ (4 x 106) = ?

(20 x 104) ÷ (80 x 106) = ?

60 = 6 x 10?

60 = 6 ÷ 10?

(103 x 106) ÷ 10-2 = ?

8 x 103 x 9 x 106 = ?

20 x 104 x 80 x 106 = ?

10? ÷ 102 = 104

7.2 x 109

the digit 7 here is the first significant figure.

the exponent is 9.

7.2 x 109

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.

How many hours does it take to drive from NYC to Chicago?

How many generations ago did Jesus Christlive?

How many shoes have you owned in your lifetime?

Examples of questions which we can answer to one significant figure

How many hours does it take to drive from NYC to Chicago?

10-12 hours

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

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

In chem speak we say

7.2 (± 0.3) x 109

the digit 7 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.

The third most important part of a number is the error bar.

0.3 is the error bar.

Significant figures is an approximate way in which scientistscommunicate 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?

Significant figures

Error bars in graphs

If unspecified, assume error bars indicate one standard deviation, s.In most cases, 1 s marks where roughly 70% of the actual events occur.

Life Spanchart forAmericans

s =15 years78 years

person

Global warming error bars

mole = 602,214,129,000,000,000,000,000.

To one significant figure what is a mole?

To one significant figure how many heart-beats 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 yearsx x x x ≈ ?

To one significant figure how many heartbeats are there in a lifetime?

1 hour

3600 seconds

1 year

365 days

1 day

24 hours

1 life

80 yearsx x x ≈ ?

1 hour

4000 seconds

1 year

400 days

1 day

20 hours

1 life

100 yearsx x x ≈ ?

1 hour

4 x 103 seconds

1 year

4 x 102 days

1 day

2 x 101 hours

1 life

1 x 102 yearsx x x ≈ 30 x 108=3 x 109

sec/life

The choo-choo train of unit conversion

1 hour

3600 seconds

1 year

365 days

1 day

24 hours

1 life

80 yearsx x x ≈ ?

1 hour

3600 seconds

1 year

365 days

1 day

24 hours

1 life

80 yearsx x x ≈ ?

blood serum normal range blood serum normal range

On a mole basis what is the most common metal ionin blood?

To 1 significant figure, please convert the Na range tomg/dL.

On a mole basis is there more creatinine or urea in blood?

even with the metric system, units get weird: the doctor's office

Ion charge x Equivalents = 1 molethis iscorrect

1 mole Ca

2 Eq Ca

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 molarimportance.

creatinine is a by-product ofmuscle degradation

C4H7N3O MW: 113.1 g mol−1

Please calculate to one significant figure the upper end creatinine levels for males in mg/dL .

creatinine

estimation

To one significant figure how many people are there in the world?

As of July 2013, there are 6,930,000,000 people in the world.

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?

How big is a mole?

Deducing answers fromknowledge we already know.

How big is the Earth?

How big is the Earth? Deducing answers fromknowledge we already know.

Always establish a strategy based on a number you know.

How big is the Earth? Deducing answers fromknowledge 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 whatsame trip at the Equator would be. Convert to kilometers.

How big is the Earth? Deducing answers fromknowledge 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 whatsame 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