Journal 8/26/14
Let’s say you need to know the temperature outside
before you get dressed for the day. You ask a friend. He
says “It’s about 50 degrees. I dunno. Maybe more,
maybe less.”
How could this be more useful or helpful?
Objective
To understand how to
mathematically manipulate
measurements
Tonight’s Homework
pp 37: 5, 6, 7, 8, 9
Notes: Significant Figures
Last time, we saw how to properly get the
precision of a measurement. Today, we’ll talk
about how we can manipulate these numbers –
addition, subtraction, multiplication, division.
Notes: Significant Figures
In addition and subtraction, we must round all
numbers to the same decimal as the least
precise number.
Example:
Add the following:
32.11 meters
76.8 meters
4.103325 meters
32.11
76.8
4.103325
113.013325
113.0 meters
Notes: Significant Figures
Multiplication and division are harder…
To start, we have to know how many
significant digits or figures a measurement
has. We use the following rules to find how
many significant digits we have.
1) Non-zero digits are always significant
2) Zeros after a decimal point that are also after
non-zeros are significant
3) Zeros between other significant digits are
significant
4) Zeros used just to space the decimal point
are not significant
Notes: Significant Figures
Examples:
143.33
15,250,000
0.0000243
0.00003001
10,000.1
0.00050
Notes: Significant Figures
Examples:
143.33
5 significant digits
15,250,000
4 significant digits
0.0000243
3 significant digits
0.00003001
4 significant digits
10,000.1
6 significant digits
0.00050
2 significant digits
Notes: Significant Figures
Think of significant digits like this…
It’s a way of measuring how many digits in a
number are important or not-rounded.
If I say 10,000,000 people, anyone reading this
knows it’s not exactly 10,000,000 people, but
something rounded.
But if I say 10,000,001 people, suddenly we
don’t assume rounding any more. Why not?
Because otherwise why would we have changed
the end to a 1 if it didn’t mean something?
Keep this in mind. It makes things easier.
Notes: Significant Figures
So how do we use this?
When multiplying and dividing, we round
everything to the number of significant digits in
the least precise measurement.
Notes: Significant Figures
So how do we use this?
When multiplying and dividing, we round
everything to the number of significant digits in
the least precise measurement.
Example:
21.7 meters x 1,000 meters
3 sig figs
1 sig fig
21,700 meters  20,000 meters
We round to 20,000 because “1,000 meters”
had only one significant digit.
Practicing Significant Figures
Let’s practice these concepts. Work with a partner and do
the following problems.
pp 37-38: 10, 11, 12, 13, 14, 15
Exit Question #5
What is the proper value of 3.22 cm times 2.1 cm?
a) 6.762 cm2
b) 6.76 cm2
c) 6.8 cm2
d) 7 cm2
e) None of the above