Transcript And Now, A Little Math

And Now, A Little Math
Hooray!!
Measurements and
Calculations
Chapter 5
Remember that the
first step in science is
making an
observation, 2 kinds
are
– Qualitative
Description based on
qualities (It is red)
– Quantitative
Measurements
2 parts – Number and
unit
Scientific Notation
Numbers used may be very large or very small
This way we can make these numbers as a product of
a number between 1 and 10 and the appropriate
power of 10
93,000,000 can be written as 9.3 x 107
– Move decimal until number is between 1 and 10 (one
number is to its left)
– Count the number of spaces you moved it
– If you moved it to the left, the number is positive
– If you moved it to the right, the number is negative
Try these
– 238,000
– 1,500,000
– 0.000167
=
=
=
2.38 x 105
1.5 X 106
1.67 x 10-4
Units
International System of Units (SI)
Based on metric system
kilo- hecto- deka- BASE deci- centi- milli-
5.3 Measurements of Length,
Volume, and Mass
Length – distance between 2 points
– Meter
– 1 inch = 2.54 centimeters
– Use rulers
Volume – space occupied by a substance
– Liter or cubic centimeters or milliliters
– Use graduated cylinders
Mass – quantity of matter in an object
– Kilogram or grams
– Use a balance
5.4 Uncertainty in Measurement
Estimate required when falls between 2
graduations
This final digit is an uncertain number
Usually record all certain numbers plus
first uncertain number
These are called the significant figures
5.5 Rules for Significant Figures
Nonzero numbers always count as significant
figures
– 1457 has 4 sig figs
Three classes of zeros
– Leading Zeros – come before nonzero
numbers are not significant
0.0025 has 2 sig figs
– Captive Zeros – between nonzero numbers
are always significant
1.008 has 4 sig figs
43,082 has 5 sig figs
– Trailing Zeros – to the right of the number are
significant only if there is a decimal point
100 has 1 but 100. has 3
470,000 has 2 sig figs but 4.00 has 3
Exact numbers – From counting or a definition
so have unlimited sig figs. Does not limit
number
– 110 riders, 8 apples, 1 inch = 2.54 cm
Rounding Off
>5 up, <5 down
In calculations, do all first and then round
Sig Figs in calculations are also important
– Multiplication or division
Sig figs same as lowest = limiting
3 sig figs x 2 sig figs = 2 sig figs
– Addition and Subtraction
Limiting has smallest number of decimals
12.11 + 18.0 + 1.013 = 31.1 (1 decimal place)