Transcript Scientific Notation and Significant Figures

Significant Figures
Density
% Error
Significant Figures
 The number of digits reported in a measurement.
 All the known digits plus one estimated value.
 The number of significant figures possible
depends upon the piece of equipment used to take
the measurement.
Significant Figures
Rules for Significant Figures
1.
2.
3.
4.
5.
Non-zero numbers are always significant.
Zeros between non-zeros are always
significant.
All final zeros to the right of the decimal
place are significant.
Zeros that act as placeholders are NOT
significant.
Counting numbers and defined constants have
an infinite number of significant figures.
Practicing Significant Figures
Determine the number of sig figs in the following numbers.
1)0.02
0.02
1
2)70001
70001
5
3)5600
5600
2
4)4.100
4.100
4
5)3.1416
3.1416 (π)
Infinite
(π)
2.80 x 105
3
6)2.80 x
Red numbers=significant
Black numbers=not significant
5
10
Rules for Rounding
If the digit to the immediate right of
the last sig fig is 5-9, round up.
If not, leave as is.
Significant Figures and
Calculators
When using a calculator, you should do the
calculation using the digits allowed by the
calculator and round off only at the end of
the problem.
Do not round off in the
middle of the problem!
Sig Figs and Addition/Subtraction
+ - + - + - + - + - + - + - +
When you add or subtract, you answer must
have the same number of digits to the right
of the decimal point as the original value
with the fewest digits to the right of the
decimal place.
+ - + - + - + - + - + - + - +
Sig Figs and Multiplication/Division
When you multiply or divide, your
answer must have the same number
of significant figures as the original
value with the least significant
figures.
Practicing Significant Figures
3.33 m2
25 m
53 mL
26.6 g
6.7 cm3
Density
Which weighs more, a
pound of bricks or a
pound of feathers?
Density
 When something feels heavy, you
are noting its density.
 Density—the mass of an object per
unit volume
Density
m
v
D=
 The unit for density should always
be some unit for mass over some
unit for volume.
 Usually it is g/mL, g/L or kg/m3
Practice Problem #1
 What is the density of an object
that has a mass of 22.5g and a
volume of 30.4 mL?
Practice Problem #2
 If a cube has sides that are 8.2 mL
each and a total mass of 46.1g,
what is its density?
Practice Problem #3
 What is the volume of isopropyl
alcohol if its mass is 45.22g and it
has a density of 0.899 g/mL?
Percent Error
A way to evaluate the accuracy of data.
Percent Error=Ratio of the error to the accepted value
│Accepted value – Measured value │
X 100%
Accepted value
Percent Error
If your measurement of a liquid is 123.4 mL
but the actual amount is 125.0 mL, what
is the percent error of the
measurement?
125.0 mL – 123.4 mL
________________________________________
125.0 mL
1.6 mL
=
_______________
125.0 mL
X 100%
=
1.3%