 # Math vs. Science to a mathematician: 73 = 73.0 = = etc

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Math vs. Science to a mathematician: 73 = 73.0 = 73.00 = 73.000 etc
to a scientist, these numbers have a more complicated meaning

Numbers in Science counts are exact and have finite number of significant figures example: this room has 30 mathematically these # are all equal: 030 = 30 = 30. = 30.0 = = not equal from chemistry point of view

dealing with large numbers of very small particles
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 by using the Atlantic and Pacific Rule

does the number have a decimal point? decimal point Absent start counting from Atlantic Ocean (right) side of # decimal point Present start counting from Pacific Ocean (left) side of #

Decimal point Absent: start counting on Atlantic (right) side
start counting with first non-zero digit & count until reach end of # 5400 m has 2 sig figs 5400 5431 5431 m has 4 sig figs

Decimal point Present:
start counting on Pacific (left) side start counting with first non-zero digit & count until reach end of # g has 7 sig figs has 4 sig figs km

sometimes, after math calculations your answer may not contain enough sig figs because… there are zeros that are not considered 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 rule 5300 cm (2 sig figs) becomes:
_

when doing calculations that involve: Multiplication and Division
final answer may only have as many sig figs as data number with least # of sig figs

correct answer: 4 24.56 cm x 14 cm = 2 sig figs 343.84 cm2 343.8 cm2

when doing calculations that involve: Addition 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 places as data number with least number of decimal places

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

correct answer: C 422.63 cm 29.472 cm 115.9 cm + 1 decimal place
________________ a) cm b) cm c) cm d) cm correct answer: C

correct answer: D NO decimals 422 cm 29 cm + 115 cm a) 566.0 cm
2 sig figs _______________ a) cm b) cm 566 cm d) cm correct answer: D

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