29 Aug 2016
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1)
2)
Significant Zeros Model 1 - Mass of Rocks
1.
Econo Balance
Sample A 100g Sample B 200g
rounded to nearest 100g
Good Balance
Sample A 140g Sample B 180g
rounded to nearest 10g (+/- 10g)
Switch and
grade - in
different
color, write in
corrections
as needed
Model 1 - Mass of Rocks
Balance Pro
Sample A 143g Sample B 177g
rounded to nearest 1g. (+/- 1g)
Exacto Balance
Sample A 143.0g
Sample B 177.1g
rounded to nearest 0.1g
(+/1 0.1g)
2pts total
½ each
Model 1 - Mass of Rocks
2. The Exacto-Balance is the best quality
instrument because... it gives the most digits
in the measurement.
or
...it measures in the smallest increments (0.1g
vs. 1g or 10g or 100g)
2pts
Model 1 - Mass of Rocks
3. Rock C is placed on the Econo Balance.
The balance reads 200g.
a) Does rock C has a mass larger or smaller
or the same as sample A, or is it impossible
to tell? Explain your reasoning.
Rock C must have a mass larger than sample
A because 200g is greater than 100g (100g
difference is enough to register on this
balance.) 2pt
Model 1 - Mass of Rocks
3. Rock C is placed on the Econo Balance.
The balance reads 200g.
b) Does rock C has a mass larger or smaller
or the same as sample B, or is it impossible to
tell? Explain your reasoning.
It is impossible to tell if rock C has a mass
larger or smaller than sample C since we do
not have enough information from the
balance. eg. If rock C were 155 or 240 the
balance would still read 200g. 2pt
Model 1 - Mass of Rocks
4. Rock C Econo 200g
Good 180g
Pro
177g
Exacto 177.0g.
a) Does rock C has a mass larger or smaller
or the same as sample B, or is it impossible to
tell? Explain your reasoning.
The Exacto balance readings suggest that
rock C has a mass that is 0.1g smaller than
rock B. However...
Model 1 - Mass of Rocks
The Exacto balance readings suggest that
rock C has a mass that is 0.1g smaller than
rock B. However, the last digit in a
measurement is always uncertain, so they
might actually be the same weight or rock C
might have a greater mass than rock B - we
need more information to be certain. An
argument can certainly be made that it is
impossible to tell which rock has the greater
mass. 2pts
4b. Explain why the zero in the
Exacto-Balance reading provides important
information about the mass of rock C, but
the zero in the Good Balance reading does
not.
The zero in the Good Balance reading is
neither a certain nor an uncertain (estimated)
digit. It is past the already rounded number “8”
and it is serving as a placeholder zero.
177.0g The zero in the Exacto-Balance
reading, however, is the uncertain (estimated)
significant digit, which does give important
information.
2pts total
Model 2 - Mass of Pebbles
5. Balance Pro Rounded to nearest 1gram
Centi balance rounded to nearest 0.01g.
Super balance rounded to nearest 0.001g
1pts total
½ each
Model 2 - Mass of Pebbles
6. Do the pebbles really have no mass?
No - their mass is less than 0.5 gram and
the balance is not sensitive enough to give
a reading for something this small.
1pt
Model 2 - Mass of Pebbles
7. Which balance is sensitive enough to
determine if pebble A has a mass larger than or
smaller than pebble B?
The Super Balance is the only balance
sensitive enough to show any difference in
mass between the pebbles.
1pt
Model 2 - Mass of Pebbles
1pt
Highlight text and answer of questions 8 key points.
0.016g Super Balance reading for A
vs
0.020 g Super Balance reading for B.
The final zero of the 2 in the reading for B is the
most significant in determining whether pebble
B has a different mass than pebble A. (Both
readings have 2 leading zeros.)
Model 3 - Types of Zeros
200g
0.02g
180g
140g
100g
0.016g
0.020g 177.0g
1pts total
½ each
“place holder”
143.0g
“significant zeros ”
9. 2 categories of zeros in measurements:
Model 3 - Types of Zeros
10. “place holder” - any others?
2pts total
1 each
11. Describe the two types of
placeholder zeros shown in Model 3.
There are place holders zeros before the
decimal point (example in 140g) and after the
decimal point (example in 0.02g)
1pt total ½
each
1pt
12. If you removed a placeholder
zero from a number, would the
numeric value of the number
change?
Example 180 g remove 0 would be 18g - not
the same size any more at all.
Removing placeholder zeros changes the
numeric value of a number.
13. Describe the location of significant zeros in a
number relative to the decimal point.
Example 0.020g 177.0g 143.0g
Significant zeros in a number are to the right of
the decimal point and at the end of a number or
between two other significant digits eg. 0.306.
14. The is no change in numeric value if a
significant zero is removed from the end of a
number! Example
177.0g becomes 177g - still the same “size.”
2pts total 1 each
Underline the zeros that are
significant in the measurements.
15.
3pts total 1 each
b. 42.0s
d. 3.000 kg
f. 0.00560 cm
All others are placeholders
16.
Rule 1. All non-zero numbers are
significant.
Set D 589 s, 45 kg , 5.68kg , 0.452 L note
Rule 2.
Sandwiched zeros (those that occur
between two significant digits) are
significant. Set A. 105 cm, 0.402g,
4003.7 mL, 10.0s
Rule 3. Zeros that are only placeholders
for a decimal are not significant.
Set B 6300mL s, 400m , 0.004kg ,
0.097 kg
Rule 4. Zeros at the end of a number that
also contains a decimal are significant.
Set C. 30.40m, 1.620s,
0.0400L
Rule 5. Exact numbers (no doubt or
uncertainty in the value) may be thought
of as having an infinite number of
significant digits. These include numbers
that were counted or are defined values
(i.e. conversion factors)
Set E 1 Dozen = 12 , 1 m = 100cm ,
29 students on a bus
5pts total 1 each
17. a) 0.420g Rules 1 and 4
b) 2100g Rules 1 and 3
c) 51.0 cm Rules 1 and 4
d) 590 students rule 1 and 5
e) 5,200.0g Rules 1, 2, and 4
f) 6020mg Rules 1, 2 and 3
6 pts
total
½ per
rule
(extra pt
poss. for
e, f)
18. a) 94, 000 m
b) 7200 apples (infinite, count)
c) 0.004380 g
d) 400.0 kg
3pts total ½ each
e) 80,050 s
f) 1000g= 1kg (defined values, conversion
factors)
MLA heading
/40
CB: init.
Significant Zeros
Extension Questions - Model 4
Scientific Notation. (Significant digits are
underlined.)
19. Scientific Notation
Expanded Notation
3 x 104 m
30, 000 m
3.00 x 104 m
30, 000 m
4.1 x 104 m
4.10 x 104 m
41, 000 m
41 000 m
Extension Questions - Model 4
Scientific Notation. (Significant digits are
underlined.)
19. Scientific Notation
Expanded Notation
3 x 104 m
30, 000 m
3.00 x 104 m
30, 000 m
3 x (10 x 10 x 10 x 10)m
3 x 10,000m
4.1 x 104 m
41, 000 m
4.10 x 104 m
41 000 m
4.10 x 10,000
-1
Negative exponent (10 = 1/10)
19. Scientific Notation
Expanded Notation
7 x 10-3 kg
0.007 kg
7.00 x 10-3 kg
0.00700 kg
7 x 1/(10 x 10 x 10)kg
7 x 0.001kg
9.42 x 10-3 kg
0.00942 kg
9.420 x 10-3 kg
0.009420 kg
9.420 x 0.001 kg
Refer to set A
20. Scientific Notation
3 x 104 m
3.00 x 104 m
Expanded Notation
30 000 m
30 000 m
a) The two measurements have the same
numeric value.
b) But they were not made with the same
instrument. We can see that the second
measurement has more significant digits,
suggesting that it was made with a more
sensitive instrument.
Refer to set A
20. Scientific Notation
3 x 104 m
3.00 x 104 m
Expanded Notation
30 000 m
30 000 m
a) The two measurements have the same
numeric value.
b) But they were not made with the same
instrument. We can see that the second
measurement has more significant digits,
suggesting that it was made with a more
sensitive instrument.
Look at all the measurements.
21. When a number in scientific notation is
changed to expanded notation the added zeros
are not significant.
For example 4.10 x 104m = 41, 000 m
The zeros added are place holder zeros and not
significant zeros.
For example 9.42 x 10-3kg = 0.00942 kg
The zeros added in front of the 942 are place
holder zeros and not significant zeros.
Look at all the measurements.
22. When a number in scientific notation contains
a significant zero, that zero is also significant in
the expanded notation.
For example 4.10 x 104m = 41, 000 m
For example 9.42 x 10-3kg = 0.00942 kg
Look at all the measurements.
22. When a number in scientific notation contains
a significant zero, that zero is also significant in
the expanded notation.
For example 4.10 x 104m = 41, 000 m
Add this
For example 9.42 x 10 kg = 0.00942
kg key
important
Scientific Notation
fact to the page
Multiple of two factors:
A factor between 1 and 10 (all digits recorded
here are significant) multiplied by ten raised
to a power or exponent.
-3
23. Scientific Notation
Expanded Notation
a)
5.078 x 106 g = 5, 078, 000 g
5.078 x 1000000g
b)
4.800 x 10-4 L = 0.0004800 L
4.800 L
1000
23. Scientific Notation
Expanded Notation
c) 0.7200 x 104 mm = confusing since not really
scientific notation - should be number between 1
and 10
d) 3 700 x 10-3 cm = again not scientific notation
23. Scientific Notation
Expanded Notation
c) 0.7200 x 104 mm = NOTE not really scientific
notation - should be number between 1 and 10
7.200 x 103 mm = 7.200 x 1000mm = 7, 200mm
23. Scientific Notation
Expanded Notation
d) 3 700 x 10-3 cm = again not scientific notation
3.700 x 100 cm = 3.700 x 1 cm = 3.700 cm
Scientific Notation Practice
https://janus.astro.umd.edu/astro/scinote/
http://lasp.colorado.edu/~bagenal/MATH/math1
.html
Let me know if you find even more helpful
resources.