Transcript Significant Figures and Scientific Notation Power Point

Scientific
Organization
of
Measurements
Significant Digits and Scientific
Notation
Significant Digits
consist of all of the digits
known with certainty plus
one final digit that is
estimated
Many experiments in science involve measuring different quantities. No
matter how carefully scientists measure something, there is always a limit to how
exact, or precise, a measurement is. This limits how precise the results of the
experiment are. For this reason, scientists use significant figures to keep track of
the precision of their calculations.
Significant Digits
Zeros appearing between nonzero digits are
significant
a) 40.7 L has three sig figs
b) 87 009 km has five sig figs
Zeros appearing in front of nonzero digits are not
significant
a) 0.095 987 m has five sig figs
b) 0.0009 kg has one sig fig
Zeros at the end of a number and to the right of a
decimal are significant
a) 85.00 g has four sig figs
b) 9.000 000 000 mm has 10 sig
figs
Zeros at the end of a number but to the left of a
decimal may or may not be significant. If such a
zero has been measured, or is the first estimated
digit, it is significant. On the other hand, if the
zero has not been measured or estimated but is
just a placeholder, it is not significant. A decimal
placed after the zeros indicates that they are
Significant.
a) 2000 m may contain from
one to four sig figs,
depending on how many
zeros are placeholders.
b) 2000. m contains four sig figs,
indicated by the presence of
the decimal point
Find the number of significant digits:

a. 0.003 26

b. 39 010

a. 3

b. 4
c. 6
d. 5

c. 77 900.1


d. 1.5300

Calculations with Sig Figs

Adding and Subtracting with Significant Figures
The answer must have the same number of digits to the
right of the decimal as there are in the measurement
having the fewest digits to the right of the decimal point.

Multiplication and Division with Significant
Figures
The answer can have no more sig figs than are in the
measurement with the fewest total sig figs
Express each answer to the correct
number of significant figures


1. 3.45 cm3 + 8.0654 cm3
2. 8.9 kg/L x 0.9753 L

3. 46.98 m – 18.114 m

4. 28 m x 16.45 m

5. 418.20 g /63.9 cm3





1. 11.52
cm3
2. 8.7 kg
3. 28.87 m
4. 460 m2
5. 6.54
g/cm3
Scientific Notation

A method of representing very large or
very small numbers
M x 10n



M is a number between 1 and 10
n is an integer
all digits in M are significant
Science often deals with large numbers. The number of hydrogen atoms in a liter
of water, for example, is almost 70 000 000 000 000 000 000 000 000. On the
other hand, the width of our galaxy is 9 315 000 000 000 000 km. To write out
such huge numbers every time you used them would be a lot of trouble. If you
were performing a series of calculations, working with long numbers could be timeconsuming and confusing.
Convert the following
measurements to scientific
notation:
a. 325 kg

3.25 x 10

4.6 x 10
c. 7104 km

7.104 x 10
d. 0.0028 L

2.8 x 10
b. 0.000 46 m
2
-4
-3
3
Scientific Notation

Reducing to Scientific Notation
1. Move decimal so that M is between 1 and 10
2. Determine n by counting the number of places
the decimal point was moved
a. Moved to the left, n is positive
b. Moved to the right, n is negative
Mathematical Operations Using Scientific
Notation

1. Addition and subtraction


2. Multiplication



Operations can only be performed if the exponent on
each number is the same
M factors are multiplied
Exponents are added
3. Division


M factors are divided
Exponents are subtracted (numerator - denominator)
Solve the following
1. (2.8 x 10 5)(7.53 x 10 -6)
________________________
2. (3.1 x 10 -2) (4.380 x 10 3)
________________________
3. (4.20 x 10 2) (0.040 x 10 -1)
________________________
4. 3.0 x 10 3 ÷ 1.2 x 10 4
________________________
5. 4.95 x 10 6 ÷ 2.33 x 10 -2
________________________

1. (2.8 x 10 5)(7.53 x 10 -6)


2. (3.1 x 10
-2)
3)
(4.380 x 10



3. (4.20 x 10
2)
(0.040 x 10
-1)



4. 3.0 x 10

5. 4.95 x 10
÷ 1.2 x 10
3
6
4
÷ 2.33 x 10
-2
2.1 x 10 0
1.4 x 10 2
1.7 x 10 0
2.5 x 10 -1
2.12 x 10 8