math vs. science mathematicianto a mathematician: 73 = 73.0 = 73.00 = 73.000 etc scientistto a...
TRANSCRIPT
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)
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…
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