Standard Form Number Sense. “135 000 will get family care soon” The actual number of families...
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Transcript of Standard Form Number Sense. “135 000 will get family care soon” The actual number of families...
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
Rounded to the
nearest
Correct choice
Number of sig. fig.
152 508 100 000 200 000 1
152 508 10 000
152 508 1 000
152 508 100
152 508 10
Complete the table.
Actual number
Rounded to the
nearest
Correct choice
Number of sig. fig.
152 508 100 000 200 000 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 Fee ($) Rounded to nearest
Rounded fee
Sig. Fig.
Electrician 1299.89 $1 4
Surgeon 1303 $10
Solicitor 1297 $100
Complete the table.
Service Fee ($) Rounded to nearest
Rounded fee
Sig. Fig.
Electrician 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 Yes
• 98 x 102 No
• 980 x 101 No
• 3.4 x 105 Yes
• 0.34 x 106 No
• 0.034 x 107 No
• 11.8 x 108 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 Rounded to nearest
Number sig. fig.
Standard form
400.00 Cent 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 Rounded to nearest
Number sig. fig.
Standard form
400.00 Cent 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
€
127
Complete the table
32 9 3-2 1/9
31 3 3-1 1/3
30 1 3-3
€
127
Write the following as fractions.
• 5-2
• 2-5
• 5-3
• 10-3
• 6-1
€
1251321
1251
100016
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.
• 1011
€
4.61×10−4
3.921×10−15≈
Estimate and then work out the following.
€
1.904×107
4.332×1019≈
€
12×1012
Estimate and then work out the following.
€
1.904×107
4.332×1019≈
€
12×1012