58%
1.
2.
Yes
No
42%
1
2
 Accuracy
- How close a measurement is
to the true value
 Precision
- How close a set of
measurements are to one another.
0%
1.
32%
2.
5%
3.
63%
4.
Accurate
Precise
Both
Neither
0%
1.
95%
2.
5%
3.
0%
4.
Accurate
Precise
Both
Neither
40%
1.
5%
2.
50%
3.
5%
4.
Accurate
Precise
Both
Neither
Write each power of ten
in standard notation.
100%
3
10
a) 30
b) 100
c) 1000
00
10
0
0%
10
30
0%
Write each power of ten
in standard notation.
90%
6
10
a) 60
b) 1000000
c) 10000
10%
0
00
10
10
00
60
00
0
0%
Write each power of ten
in standard notation.
17%
0
.0
1
17%
10
a) .01
b) -20
c) 100
-2
0
-2
10
67%
Write each power of ten
in standard notation.
100%
-4
10
a) -.0004
b) .0004
c) 10000
0
00
10
04
0%
.0
0
-.0
00
4
0%
Setting the Stage
• There are
325,000 grains
of sand in a
tub. Write that
number in
scientific
notation.
What is the exponent to the 10
for 325,000 grains of sand?
53%
0%
47%
0%
0%
0%
0%
1.
2.
3.
4.
5.
6.
7.
3
4
5
6
-6
-5
-4
Definition
• Scientific notation- is a compact
way of writing numbers with
absolute values that are very large
or very small.
•
Glencoe McGraw-Hill. Math connects cours 3. pages 130-131
 all
numbers are expressed as whole
numbers between 1 and 9 multiplied by a
whole number power of 10.
 If
the absolute value of the original
number was between 0 and 1, the
exponent is negative. Otherwise, the
exponent is positive.
• Ex. 125 = 1.25 x 102
• 0.00004567 = 4.567 x 10-5
7%
1.
87%
2.
0%
3.
0%
4.
7%
5.
0%
6.
-6
6
-5
5
4
-4
0%
1.
0%
2.
6%
3.
11%
4.
11%
5.
72%
6.
-6
6
-5
5
4
-4
What is 2.85 x 104 written in
standard form
.000285
285
28500
2850
88%
28
28
50
0
5
50
6%
0%
28
02
85
6%
.0
0
A.
B.
C.
D.
7
10
What is 3.085 x
written in
standard form
.0000003085
30,850,000
3085
308,500,000
77%
15%
8%
00
85
30
85
00
0
30
0
00
0
85
30
00
00
30
85
0%
.0
0
A.
B.
C.
D.
-3
10
What is 1.55 x
written in
standard form
.00155
155
1550
.000155
94%
6%
0%
.0
0
01
55
50
15
5
15
15
5
0%
.0
0
A.
B.
C.
D.
-2
10
What is 2.7005 x
written in
standard form
A.
B.
C.
D.
270.05
27005
.27005
.027005
Write the following numbers in scientific
notation:
A) 5,000
E) 0.0145
B) 34,000
F) 0.000238
C) 1,230,000
G) 0.0000651
D) 5,050,000,000 H) 0.000000673
Closure / Summary
• Explain why 32.8 x 104 is not correctly
written in scientific notation.
• What does a negative exponent tell you
about writing the number in standard form.
 Significant
Figures are used to show the
accuracy and precision of the
instruments used to take the
measurement.
1
0
0%
1.
0%
2.
0%
3.
0%
4.
0.55
0.7
0.6
0.8
1
0
0%
1.
0%
2.
0%
3.
0%
4.
0.55
0.70
0.67
0.65
 To
show how precise the instrument is:
• Read the measurement to one decimal place
what the instrument is marked
0%
1.
0%
2.
0%
3.
0%
4.
4.85
7.2
4.3
4.35
0%
1.
0%
2.
0%
3.
0%
4.
17.0
16.8
15.18
15.2
 Non-zero
digits are always significant
1,2,3,4,5,6,7,8,9 are always significant
 Rules
for Zeros:
a) Leading Zeros never count as significant
0.0000456
0.0032
b) Captive zeros (zeros between non-zero digits) are
always significant
10,034
0.005008
c) Trailing Zeros are significant ONLY IF there is a
decimal in the number.
234,000
234,000.0
0.045600
 If
we want to write the number 700 with 3
significant digits we can do so using the
following two methods:
700. OR
7.00×102
0%
1.
0%
2.
0%
3.
0%
4.
1
2
3
0
0%
1.
0%
2.
0%
3.
0%
4.
0
1
2
3
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
3
1
6
7
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
2
5
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
1
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
1
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
5
8
2
4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
5
8
2
4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0%
1.
0%
2.
0%
3.
0%
4.
1
2
21
22
3
3
8
4
5
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
 Count
(from left to right) how many
significant figures you need.
 Look at the next number to see if you need
to round your last sig. fig. up or down.
Round the following to 3 sig. figs
1. 1,344
2. 0.00056784
3. 24,500
4. 12,345
5. 2.45678 x 10-3
We have two ways of categorizing sig. fig.
calculations:
A) Addition and Subtraction
B) Multiplication, Division, other math
When we add and subtract we are only
worried about the number of decimal
places involved in the numbers present.
We do not care about the number of
actual significant digits.
We will always pick the number that has
the least decimal places.
A) 14.0 + 2.45
B) 12 + 7.2
C) 0.00123 + 1.005
D) 100 – 5.8
E) 2.5 – 1.25
F) 43.786 – 32.11
If we are multiplying, dividing, using
exponents, trigonometry, calculus, etc we
must use the least number of significant
digits of the numbers in the set.
For example...
A) 12 × 5.00
B) 8.45 × 4.3
C) 0.0125 × 7.532
D) 5.6 × 11.7
E) 34.1 × 0.55
F) 119 / 32
G) 756.2 / 29.8
H) 0.976 / 0.0044
I ) 981 / 756.23
J) 43.2 / 12.45
 Density
– the amount of matter present
in a given volume of a substance, the
ratio of the mass of an object to its
volume.

D = mass

Volume
 Celsius Scale – based on the freezing point
(0oC) and boiling point (100oC) of water.
 Kelvin
Scale – based on absolute zero (the
temperature at which all motion ceases). 1
degree Kelvin is equal to 1 degree Celsius.
 Fahrenheit
Scale – used in US and Great
Britain. Degrees are smaller than a Celsius
or Kelvin degree.
 Kelvin/Celsius
K = oC + 273
 Fahrenheit/Celsius
oF
= 1.80(oC) + 32
 Exact
Numbers are counting numbers or
defined numbers (such as 2.45 cm = 1 in)
- never limit the number of significant
figures in a calculation.