a digit that is reliably known Ex 62 has 2 sig figs The hundredth place is not reliably known and thus not reported The easiest way to determine sig figs in a number is to write the number in scientific notation ID: 645666
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Slide1
Sig FigsSlide2
Significant figure
a digit that is reliably known.
Ex: 6.2 has 2 sig figs. The hundredth place is not reliably known and, thus, not reported.Slide3
The easiest way to determine
sig figs in a number
is to write the number in scientific notation.
0.00620 = 6.20 x 10
-3
The trailing zero is reliably known, so it is SIGNIFICANT.
The number of significant figures is the number of digits when written in
sci
notation.Slide4
Some Rules for Sig Figs
The number of sig figs
does not equal
the number of decimal places.
In whole numbers, trailing zeroes
are not
sig figs.
Ex: 320,000 is 3.2 x 10
5
It has 2 sig figs.
Changing units may shift the decimal points but it doesn’t change the number of sig figs. Slide5
When multiplying/dividing (or taking roots), the number of sig figs in the answer should match the number of sig figs of the
least
precise number in the calculation.
When adding/subtracting, the number of sig figs in the answer should match the
smallest
amount of decimal places of any number in the calculation.Slide6
It’s fine to keep extra numbers around in the intermediate steps, but your final answer
MUST
be accurate in terms of significant figures.
Otherwise, you’ve performed magic and have something more accurate that we can verify.Slide7
Example
The volume of a piece of Al is 4.44 x 10
-4
m
3
. Given a density of 2.7 x10
3
kg/m
3
, what is the total mass of the piece of Al? (mass = density x volume)Slide8
m=
4.44 x 10
-4
m
3
(
2.7 x10
3
kg/m
3
)
m= 1.199 kg
m= 1.2 kgSlide9
If we have a second mass of Al, measured to be 6.47 kg, how much total Al do we have?Slide10
`
6.47 kg + 1.2 kg
=
7.7 kg