Transcript Math Skills for the Laboratory

Measurement Systems
Why do we need a measurement system?
Scientific Notation
A way to write very large and very small
numbers.
A number in scientific notation is written in two
parts, the coefficient and an exponent of 10.
coefficient
5 x 1022
exponent of 10
Scientific Notation
Changing standard numbers to scientific notation
1.
Numbers greater than 10
a. Move decimal until only ONE number is to the
left of the decimal.
b. The exponent is the number of places the
decimal has moved and it is POSITIVE.
Ex. 125 = 1.25  102
15,000,000,000 = 1.5  1010
Scientific Notation
Changing standard numbers to scientific notation
2.
Numbers less than 1
a. Move decimal until only one number is to the
left of the decimal.
b. The exponent is the number of places the
decimal has moved and it is NEGATIVE.
Ex. 0.000189 = 1.89  10-4
0.5476 = 5.476  10-1
Scientific Notation
Changing standard numbers to scientific notation
3.
To change a number written in incorrect scientific
notation:
a. Move the decimal until only one number is to
the left of the decimal.
b. Correct the exponent. (remember: take away,
add back)
coefficient decreased by 2, so
Ex. 504.2  106 = 5.042  108 The
the exponent must increase by 2
0.0089  10-2 = 8.9  10-5
The coefficient increased by 3, so
the exponent must decrease by 3
Scientific Notation
Changing numbers in scientific notation to
standard notation
1.
2.
If the exponent is (+) move the decimal to the right
the same number of places as the exponent.
a. 1.65  101 = 16.5
b. 1.65  103 = 1650
If the exponent is (-) move the decimal to the left the
same number of places as the exponent.
a. 4.6  10-2 = 0.046
b. 1.23  10-3 = 0.00123
Scientific Notation
Multiplication and Division in Scientific Notation
1.
To multiply numbers in scientific notation
a. Multiply the coefficients.
b. Add the exponents.
c. Convert the answer to correct scientific
notation.
Ex: (2  109) x (4  103) = 8 x 1012
Scientific Notation
Multiplication and Division in Scientific Notation
2.
To divide numbers in scientific notation
a. Divide the coefficients.
b. Subtract the exponents.
c. Convert the answer to correct scientific
notation.
Ex: (8.4  106)  (2.1  102) = 4 x 104
Scientific Notation
Addition and Subtraction in Scientific Notation
1. Before numbers can be added or subtracted, the
exponents must be equal.
Ex. (5.4  103) + (6.0  102)
= (5.4  103) + (0.6  103)
= 6.0  103
Significant Figures
Are all the numbers for which actual
measurements are made plus one
estimated number.
1
2
You would estimate this measurement as 1.5
1
2
You would estimate this measurement as 1.48
Significant Figures
Tells the person interpreting your data about
the accuracy of the measuring instrument used
to obtain the data.
Significant Figures
Rules for counting sig figs
1. Digits other than zero are always significant.
a. 96 = 2 sig figs
b. 61.4 = 3 sig figs
2. Zeroes between 2 other sig figs are always
significant.
a. 5.029 = 4 sig figs
b. 306 = 3 sig figs
Significant Figures
Rules for counting sig figs
3. Leading zeroes are never significant when they are
to the left of non-zero numbers.
a. 0.0025 = 2 sig figs
b. 0.0821 = 3 sig figs
4. Trailing zeroes are only significant if there is a
decimal present and they are to the right of nonzero
numbers.
a. 100 = 1 sig fig
b. 100.0 = 4 sig figs
c. 0.0820 = 3 sig figs
Significant Figures
Rules for calculating with sig figs
1.
In addition and subtraction, the answer should be rounded off
so that it has the same number of decimal places as the
quantity having the least number of decimal places.
a. 1.1 + 225 = 226.1 = 226 (rounded to no decimal places)
b. 2.65 – 1.4 = 1.25 = 1.3 (rounded to 1 decimal place)
2.
In multiplication and division, the answer should have the
same number of significant figures as the given data value
with the least number of significant figures.
a. 4.60  45 = 207 = 210 (rounded to 2 sig figs)
b. 1.956  3.3 = 0.5927 = 0.59 (rounded to 2 sig figs)
Metric System
Unit
Unit
Unit
Unit
Unit
of
of
of
of
of
length…..meter (m)
mass ……gram (g)
volume …liter (L)
time …….second (s)
temperature…degrees Celsius (°C)
Metric System
The metric system is based on units of 10.
Prefix symbol
Prefix name
Prefix value
Fraction or Multiple
Power
G
giga
one billion
1,000,000,000
109
M
mega
one million
1,000,000
106
k
kilo
one thousand
1000
103
1
10
BASIC UNIT: m, g, L,
d
deci
1/10
0.1
10-1
c
centi
1/100
0.01
10-2
m
milli
1/1000
0.001
10-3
µ
micro
1/1,000,000
0.000 001
10-6
n
nano
1/1,000,000,000
0.000 000 001
10-9
Metric System
 To convert measurements within the metric system is a
simple matter of multiplying or dividing by 10, 100,
1000, etc.
 Even simpler, it is a matter of moving the decimal point
to the left or right.
Metric System
 One way to know where to place the decimal is to draw a "metric
line" with the basic unit in the center, marking off six units to the
left and six units to the right.
 To convert from one unit to another simply count the number of
places to the left or right, and move the decimal in that direction
that many places.
Ex. 3 L = 0.003 kL
Ex. 3 mg = 3000 µg
Two Systems
English




yard, mile, feet
pound, ounce
quart, gallon
Fahrenheit
Metric




Meter
Gram
Liter
Celsius
Factor-Label
T h e m o s t i m p o r t a n t
mathematical process
for scientists.
T r e a t s n u m b e r s a n d
units equally.
M u l t i p l y w h a t i s g i v e n
by fractions equal to
one to convert units.
Factor-Label
What is given
A fraction
equal to one
Factor-Label
How many basketballs can
be carried by 8 buses?
1 bus = 12 cars
3 cars = 1 truck
1000 basketballs = 1 truck
Factor-Label
How many basketballs can
be carried by 8 buses?
8 buses
1 bus = 12 cars
3 cars = 1 truck
1000 basketballs = 1 truck
Factor-Label
How many basketballs can
be carried by 8 buses?
8 buses
12 cars
1 bus
1 bus = 12 cars
3 cars = 1 truck
1000 basketballs = 1 truck
Factor-Label
How many basketballs can
be carried by 8 buses?
8 buses
12 cars
1 truck
1 bus
3 cars
Factor-Label
How many basketballs can
be carried by 8 buses?
8 buses
12 cars
1 truck 1000 bballs
1 bus
3 cars
1 truck
Factor-Label
32000 basketballs can
be carried by 8 buses.
Factor-Label
Convert 5 pounds
to kilograms.
Factor-Label
Convert 5 pounds to kilograms
5 lb
1 kg
2 . 2 0 lb
= 2.27 kg
Factor-Label
Convert 8.3 centimeters
to millimeters.
Factor-Label
Convert 8.3 centimeters to
millimeters
8.3 cm
1m
1000 mm
100 cm
1m
=
83 mm
Factor-Label
Method