Math vs. Science

• to a mathematicianmathematician:

73 = 73.0 = 73.00 = 73.000 etc

• to a scientistscientist, these numbers have a more complicated meaning

Numbers in ScienceNumbers in Sciencecountscounts are exact and have finite number

of significant figures• example: this room has 30

mathematically these # are all equal: 030 = 30 = 30. = 30.0 = 30.00 = 30.000

not equal from chemistry point of view

significant figures are used for data calculations in chemistry because..•dealing with large numbers of very small particles

– #’s often written to power of 10 • ex: (3.26 x 10-5)

How do I determine the number of

Significant Figures?

P

A

the easiest way to count sig figs is the easiest way to count sig figs is by using the by using the Atlantic and Pacific Atlantic and Pacific RuleRule

11stst ask yourself this question:ask yourself this question:

does the number have a decimal pointdoes the number have a decimal point? ?

decimal point decimal point AAbsentbsent start counting start counting fromfrom AtlanticAtlantic Ocean (right) side of # Ocean (right) side of #

decimal point decimal point PPresentresent start counting from start counting from PacificPacific Ocean (left) side of #Ocean (left) side of #

Decimal point Absent:•start counting on Atlantic (right) side

•start counting with first non-zero non-zero digit & count until reach end of #

5400 m has 22 sig figs

5431 m

has 44 sig figs

5400

5431

Decimal point Present:

• start counting with first non-zeronon-zero digit & count until reach end of #

2545.300 g

0.004530 km

has 77 sig figs

has 44 sig figs

•start counting on Pacific (left) side

2545.300

0.004530

sometimes,after math calculations youranswer may not contain enoughsig figsbecause… there are zeros that are notconsidered significant

ex:if calc answer is 5300, but need 3 sig

figs…

if you want a zero to be significant draw a line above to show that it is significant

once in a BLUE MOON BLUE MOON rulerule

5300 cm (2 sig figs) becomes:

5300 cm (3 sig figs)

_

when doing calculations that involve:

Multiplication Multiplication and Divisionand Division

final answer may only have as many sig figssig figs as data number with least #least # of sig figs

24.56 cm x 14 cm =

1. 343.84 cm2

2. 343.8 cm2

3. 343 cm2

4. 340 cm2

correct correct answer: answer: 44

2 sig figs

when doing calculations that involve:

Addition and SubtractionAddition and Subtraction

2 possibilities:

1st need to look & see if any of the data numbers have decimals present

1. If ALL data # have decimals:

final answer may only have as many decimal placesdecimal places as data number with least numberleast number of decimal places

2. If some or NO decimals present: final answer may only have as many significant figuressignificant figures as data number with least numberleast number of sig figs

422.63 cm 29.472 cm 115.9 cm________________+

a) 568.002 cm

b) 568.00 cm

c) 568.0 cm

d) 568 cm

correct correct answer: Canswer: C

1 decimal place

422 cm 29 cm + 115 cm

_______________

a) 566.0 cm

b) 566. cm

c) 566 cm

d) 570 cm

NO decimals2 sig figs

correct correct answer: Danswer: D