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