Transcript scientific notation

Chemistry
Wilbraham
Staley
Matta
Waterman
Chapter 3: Scientific Measurement
Copyright © 2005 Pearson Education & Prentice-Hall, Inc.
Prompt:
When you make a measurement, what are
some possible sources of uncertainty?
How do you write numbers in scientific
notation?
Measurement: is a quantity that has both a
number and a unit.
examples:
height (66 inches)
age (15)
body temperature (37oC).
a gram of hydrogen, for example=
602,000,000,000,000,000,000,000 hydrogen
atoms.
The mass of an atom of gold =
0.000000000000000000000327 gram.
Work more easily with number by writing them
in scientific notation.
scientific notation: a given number is written
as the product of two numbers: a coefficient
and 10 raised to a power.
For example,
602,000,000,000,000,000,000,000 can be
23
written in scientific notation as 6.02 x 10
The coefficient in this number is 6.02, the
power of 10, or exponent, is 23.
In scientific notation, the coefficient is always
a number greater than or equal to one or less
than ten. The exponent is an integer.
Positive exponent: indicated how many
times the coefficient must be multiplied by 10.
Negative exponent: indicated how many
times the coefficient must be divide by 10.
Larger than 10?
Positive exponent!
the exponent must be divided by 10
6, 300,000 = 6.3 x 106
94,700 = 9.47 x 104
equals the number of places that the original decimal point
has been moved to the left.
Less than 10
Negative Exponent!
0.000 008 = 8 x 10-6
0.0736 = 7.36 x 10-3
The value of the exponent equals the number of places the
decimal has moved to the right.
Multiplication
Multiplication of numbers in scientific notation:
multiply the coefficients and add the exponents
(3 x 104) x (2 x 102) = (3x 2) x 104+2 = 6 x 106
(2.1 x 103) x (4.0 x 10-7) = (2.1 x 4) x 103+(-7) = 8.4 x 10-4
Division
To divide numbers written in scientific notation
divide the coefficient and subtract the exponent in the
denominator from the exponent in the numerator.
(3 x 105) / (6.0 x 102) = (3.0 / 6.0) x 105-2 = 0.5 x 103 = 5.0 x
102
Addition and subtraction
if you are not using a calculator
then exponents must be the same.
(5.4 x 103) + (8.0 x 102) = first rewrite the second number so
equation is a 3.
(5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103)
(5.4 + 0.08) x 103
= 6.2 x 103
Using Scientific Notation
Solve in your notes:
a. (8.0 x 10-2) x (7.0 x 10-5)=
b. (7.1 x 10-2) + (5 x 10-3)=
a. (8.0 x 10-2) x (7.0 x 10-5)= (8.0 x 7.0) x 10-2 (-5)= 56 x 10-7
= 5.6 x 10-6
b. (7.1 x 10-2) + (5 x 10-3)= (7.1 x 10-2) + (0.5 x 10-2)
= 7.6 x 10 -2
Accuracy, Precision and Error
How do you evaluate accuracy and precision?
In groups of 2-3 students, use a meter-stick
and a metric ruler to measure the height of the:
wall
deck
front bench
to the nearest meter, centimeter, or
millimeter.
Make a table for your data!
m
Wall
Deck
Bench
cm
mm
When finished:
Compare your results- Make a larger table on
the white board, and write your findings in the
appropriate locations.
Measurements can be correct but have
degrees of uncertainty.
Were the measurements for each
type of units the same?
Which unit provided the most
accurate data?
Millimeters provides the closest measurement
to the actual length.