Transcript File

Standard Form
Number Sense
“135 000 will get family care soon”
• The actual number of families granted
family care is 135 148.
• This number has been rounded by the
reporter to 135 000.
• How many significant figures are there
in the rounded number?
“135 000 will get family care soon”
• The actual number of families granted
family care is 135 148.
• This number has been rounded by the
reporter to 135 000.
• How many significant figures are there
in the rounded number?
• 3 as the number is rounded to the
nearest thousand.
“145 000 applications have
been processed.”
• What is the lowest number of
applications that this number
represents?
• What is the highest number of
applications that this number
represents?
“145 000 applications have
been processed.”
• What is the lowest number of
applications that this number
represents? 144 500
• What is the highest number of
applications that this number
represents? 145 499
Complete the table.
Actual
number
152 508
Rounded
to the
nearest
100 000
152 508
10 000
152 508
1 000
152 508
100
152 508
10
Correct
choice
Number of
sig. fig.
200 000
1
Complete the table.
Actual
number
Correct
choice
Number of
sig. fig.
152 508
Rounded
to the
nearest
100 000
200 000
1
152 508
10 000
150 000
2
152 508
1 000
153 000
3
152 508
100
152 500
4
152 508
10
152 510
5
A sack of coal weighs 50 kg to
the nearest kilogram.
• What weights would be acceptable for
the following?
• The least weight.
• The greatest weight.
A sack of coal weighs 50 kg to
the nearest kilogram.
• What weights would be acceptable for
the following?
• The least weight. 49.5 kg
• The greatest weight. 50.4999… kg
A sack of coal weighs 50 kg to
the nearest kilogram.
• Which of these weights represents a
short weighing?
• 49.6 kg
• 49.4 kg
• 49.49 kg
• 49.5 kg
A sack of coal weighs 50 kg to
the nearest kilogram.
• Which of these weights represents a
short weighing?
• 49.6 kg
• 49.4 kg - will round to 49 kg
• 49.49 kg - will round to 49 kg
• 49.5 kg
An AA sign tells motorists that
Hamilton is 56 km away.
• Where in Hamilton is the distance 56
km measured to?
• A motorist checks her odometer and
notes the distance to be 55.8 km. Who
is correct, the motorist or the AA?
An AA sign tells motorists that
Hamilton is 56 km away.
• Where in Hamilton is the distance 56 km
measured to? The central post office.
• A motorist checks her odometer and notes
the distance to be 55.8 km. Who is correct,
the motorist or the AA?
• Both are correct. The AA has rounded the
distance to the nearest whole number.
Complete the table.
Service
Electrician
Fee ($) Rounded Rounded Sig.
to
fee
Fig.
nearest
1299.89
$1
4
Surgeon
1303
$10
Solicitor
1297
$100
Complete the table.
Service
Electrician
Fee ($) Rounded Rounded Sig.
to
fee
Fig.
nearest
1299.89
$1
$1300
4
Surgeon
1303
$10
$1300
3
Solicitor
1297
$100
$1300
2
Standard Notation
(Scientific Form)
• 10 000 000 000 000.
• This number does not fit into most
calculators.
• The number can be written as 1013 or
• 1 x 1013.
Write the following numbers in
power form.
• The distance to the nearest star is about
10 000 000 000 000 km.
• When 1 kg of mass is completely
converted to energy it produces about
100 000 000 000 000 joules of energy.
• The number of atoms in your body is
about 1 000 000 000 000 000 000 000
000 000.
Write the following numbers in
power form.
• The distance to the nearest star is about 10
000 000 000 000 km. 1013
• When 1 kg of mass is completely converted
to energy it produces about 100 000 000 000
000 joules of energy. 1014
• The number of atoms in your body is about 1
000 000 000 000 000 000 000 000 000. 1027
Write the following in decimal
form.
•
•
•
•
•
3.6 x 10 =
3.6 x 102 =
3.6 x 103 =
4.3 x 105 =
1.03 x 107 =
Write the following in decimal
form.
•
•
•
•
•
3.6 x 10 = 36
3.6 x 102 = 360
3.6 x 103 = 3600
4.3 x 105 = 430 000
1.03 x 107 = 1 030 000
Standard form
• 9.63 x 104 is in standard form.
• 96.3 x 103 is not in standard form.
Which of the following are in
standard form?
•
•
•
•
•
•
•
9.8 x 103
98 x 102
980 x 101
3.4 x 105
0.34 x 106
0.034 x 107
11.8 x 108
Which of the following are in
standard form?
•
•
•
•
•
•
•
9.8 x 103
98 x 102
980 x 101
3.4 x 105
0.34 x 106
0.034 x 107
11.8 x 108
Yes
No
No
Yes
No
No
No
Write the following in scientific
notation (standard form)
• The speed of light ≈ 300 000 000 m/s
• The volume of the earth ≈
1 080 000 000 000 cubic kilometres.
• The length of the equator ≈ 40 020 km.
• The distance sound travels in one
minute ≈ 19 700 m.
Write the following in scientific
notation (standard form)
• The speed of light ≈ 300 000 000 m/s
• 3 x 108
• The volume of the earth ≈
1 080 000 000 000 cubic kilometres.
1.08 x 1012
• The length of the equator ≈ 40 020 km.
• 4.002 x 104
• The distance sound travels in one minute ≈
19 700 m. 1.97 x 104
Complete the table.
(Sig. fig. are underlined)
Amount
400.00
Rounded
to nearest
Cent
Number
Standard
sig. fig.
form
5
4.0000 x 102
400.00
400.00
4.00 x 102
400.00
400.00
4 x 102
Complete the table.
(Sig. fig. are underlined)
Amount
400.00
Rounded
to nearest
Cent
Number
Standard
sig. fig.
form
5
4.0000 x 102
400.00
10 c
4
4.000 x 102
400.00
$1
3
4.00 x 102
400.00
$10
2
4.0 x 102
400.00
$100
1
4 x 102
Light from the Great Galaxy in Andromeda
takes about 2.3 x 106 years to reach Earth.
Light travels at about 2.998 x 105 km/s.
• How many sig. fig. in 2.3 x 106?
• How many sig. fig. in 2.998 x 105?
• How many seconds are there in 2.3 x 106
years?
• Round your answer to 2 sig. fig.
• Distance = speed x time. What is the distance
from Earth to the Great Galaxy in
Andromeda?
Light from the Great Galaxy in Andromeda
takes about 2.3 x 106 years to reach Earth.
Light travels at about 2.998 x 105 km/s.
• How many sig. fig. in 2.3 x 106? 2
• How many sig. fig. in 2.998 x 105? 4
• How many seconds are there in 2.3 x 106
years? 2
• Round your answer to 2 sig. fig.
• Distance = speed x time. What is the distance
from Earth to the Great Galaxy in
Andromeda? 2.3 x 106 x 365.25 x 24 x 60 x 60 x
2.998 x 105 = 2.2 x 1019 km
The speed of light is about
2.998 x 105 km/s.
• Light from the Sun takes 5.00 x 102
seconds to reach Earth. How far is the
Earth from the Sun? (Round sensibly.)
The speed of light is about
2.998 x 105 km/s.
• Light from the Sun takes 5.00 x 102
seconds to reach Earth. How far is the
Earth from the Sun? (Round sensibly)
2.998 x 105 x 5.00 x 102 = 1.50 x 108 km
Rounded to 3 sig. fig.
The surface area of a sphere of radius r is
about (1.2566 x 101) x r2. The radius of the
earth is about 6.37 x 106 metres.
• Find the surface area of the earth in
• A. square metres
• B. square kilometres
The surface area of a sphere of radius r is
about (1.2566 x 101) x r2. The radius of the
earth is about 6.37 x 106 metres.
• Find the surface area of the earth in
• A. square metres 5.64 x 1014
• B. square kilometres 5.64 x 108
Write in power form
0.01
0.000 01
0.001
0.1
0.000 000
000 1
0.000 000
000 01
Write in power form
0.01
10-2
0.000 01
10-5
0.001
10-3
0.1
10-1
0.000 000
000 1
10-10
0.000 000
000 01
10-11
Complete the table
22
2-2
21
2-1
20
2-3
Complete the table
22
4
2-2
1/4
21
2
2-1
1/2
20
1
2-3
1/8
Complete the table
32
3-2
31
3-1
30
3-3
1
27
Complete the table
32
9
3-2
1/9
31
3
3-1
1/3
30
1
3-3
1
27
Write the following as
fractions.
• 5-2
• 2-5
• 5-3
• 10-3
• 6-1
1
25
1
32
1
125
1
1000
1
6
Write the following in standard
form
•
•
•
•
•
0.071
0.0073
19.04
0.0000346
0.02003
•
•
•
•
•
7.1 x 10-2
7.3 x 10-3
1.904 x 10-1
3.46 x 10-5
2.003 x 10-2
A proton is moving at 2.8 x 108
m/s in a cyclotron.
• How far will the
proton travel in 3.2 x
10-5 seconds?
A proton is moving at 2.8 x 108
m/s in a cyclotron.
• How far will the
proton travel in 3.2 x
10-5 seconds?
• 8960 m
• = 9.0 x 103 m
• (2 sig. fig.)
Another proton moves 2.3 x
10-1 m in 9.7 x 10-5 s.
• What is its speed
(to 2 sig. fig.)?
Another proton moves 2.3 x
10-1 m in 9.7 x 10-5 s.
• What is its speed
(to 2 sig. fig.)?
2371 m/s
= 2.4 x 102 m/s
Complete this estimate.
4
4.6110
11
•
10

15
3.92110
Estimate and then work out
the following.
1.904 10

19
4.332 10
7
1
12
2 10
Estimate and then work out
the following.
1.904 10

19
4.332 10
7
1
12
2 10