Transcript ScientificMeasurementx

Scientific Measurement
Significant Figures
 Measurements should be reported using the correct number
of digits so they do not appear to be more accurate than they
actually are
 Significant figures are the numbers in a measurement that
actually mean something, or can be trusted.
123
123.0
0.0123
three significant figures
four significant figures
three significant figures
Rules: Significant Figures
1.
All nonzero digits are significant:
1.234 g has 4 significant figures
1.2 g has 2 significant figures
2.
Zeroes between nonzero digits are significant:
1002 kg has 4 significant figures
3.07 mL has 3 significant figures
3.
Leading zeros to the left of the first nonzero digits are not
significant and merely indicate the position of the decimal
point:
o
0.001 C has only 1 significant figure
0.012 g has 2 significant figures
Rules: Significant Figures
4.
Trailing zeroes that are also to the right of a decimal point
in a number are significant:
0.0230 mL has 3 significant figures
0.20 g has 2 significant figures
5.
When a number ends in zeroes that are not to the right of a
decimal point, the zeroes are not necessarily significant:
190 miles may be 2 or 3 significant figures
50,600 calories may be 3, 4, or 5 significant figures
Rules: Mathematical Operations
 In addition and subtraction, the result is rounded off so that it
has the same number of digits as the measurement having the
fewest decimal places (counting from left to right)
100. (3 sig. figs.) + 23.643 (5 sig. figs.) = 123.643
This should be rounded to 124 (3 sig. figs.)
 In multiplication and division, the result should be rounded
off so as to have the same number of significant figures as in the
component with the least number of significant figures
3.0 (2 sig. figs.) × 12.60 (4 sig. figs.) = 37.8000
This should be rounded to 38 (2 sig. figs.)
Scientific Notation and Exponents
 Science deals with both very large and very small numbers, so
scientists often use a "shorthand" way to write these values
 Bases and Exponents
 24
 103
 10-3
 Scientific notation is a tool that uses exponents to
simplify handling numbers that are very big or very small
3400 (standard notation) = 3.4 X 103 (scientific notation)
3.4 X 10 X 10 X 10 = 3400
Writing a Number in Scientific Notation
1.
Move the decimal point so that the number is between 1 and 10.
2.
Count the number of decimal places moved in Step 1.
If the decimal point was moved to the left, the count is positive.
If the decimal point was moved to the right, the count is negative.
3.
Write as a product of the number (found in Step 1) and 10
raised to the power of the count (found in Step 2).
The general format for a number written in scientific notation is
N x 10power
Practice: Convert the number 0.000348 to scientific notation.
The Metric System
base
giga
mega
kilo
hecto
deka
meter
deci
centi
milli
micro
nano
109
106
103
102
101
1.0
gram
10-1
10-2
10-3
10-6
10-9
liter
King Henry Doesn't [Usually] Drink Chocolate Milk
Metric Conversions
 One can move from one prefix to another by moving the decimal
point one place, filling in, as necessary, with zeroes.
 To move to a smaller unit (a unit with a prefix some number of
places further to the right in the listing), move the decimal place to
the right that same number of places.
 To move to a larger unit (a unit with a prefix some number of
places further to the left in the listing), move the decimal place to the
left that same number of places.
Practice Problem 1: convert 12.54 km to cm
Unit Conversions
 In many scientific and technical applications, there is a need to
change from one type of unit to another.
 Metric system  English system
 To perform unit conversions, start with the given measure and
multiply it by the appropriate conversion factor(s) to yield the
desired units in the end.
 The denominator of the fraction should contain the unit of the
original number
 The numerator of the fraction should contain the unit you want to
change to
Unit Conversions
 Practice problem: Convert 105 lb to kg
 Known: 1 kg = 2.2 lb