standard form number sense. “135 000 will get family care soon” the actual number of families...
TRANSCRIPT
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Standard Form
Number Sense
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“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?
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“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.
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“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?
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“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
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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
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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
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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.
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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
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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
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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
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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?
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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.
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Complete the table.
Service Fee ($) Rounded to nearest
Rounded fee
Sig. Fig.
Electrician 1299.89 $1 4
Surgeon 1303 $10
Solicitor 1297 $100
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Complete the table.
Service Fee ($) Rounded to nearest
Rounded fee
Sig. Fig.
Electrician 1299.89 $1 $1300 4
Surgeon 1303 $10 $1300 3
Solicitor 1297 $100 $1300 2
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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.
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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.
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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
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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 =
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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
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Standard form
• 9.63 x 104 is in standard form.
• 96.3 x 103 is not in standard form.
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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
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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
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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.
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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
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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
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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
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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?
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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
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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.)
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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.
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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
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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
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Write in power form
0.01 0.000 01
0.001 0.1
0.000 000 000 1
0.000 000 000 01
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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
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Complete the table
22 2-2
21 2-1
20 2-3
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Complete the table
22 4 2-2 1/4
21 2 2-1 1/2
20 1 2-3 1/8
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Complete the table
32 3-2
31 3-1
30 3-3
€
127
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Complete the table
32 9 3-2 1/9
31 3 3-1 1/3
30 1 3-3
€
127
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Write the following as fractions.
• 5-2
• 2-5
• 5-3
• 10-3
• 6-1
€
1251321
1251
100016
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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
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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?
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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.)
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Another proton moves 2.3 x 10-1 m in 9.7 x 10-5 s.
• What is its speed
(to 2 sig. fig.)?
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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
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Complete this estimate.
• 1011
€
4.61×10−4
3.921×10−15≈
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Estimate and then work out the following.
€
1.904×107
4.332×1019≈
€
12×1012
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Estimate and then work out the following.
€
1.904×107
4.332×1019≈
€
12×1012