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1 The real numbers
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Australia
Year 9

1.04 Using scientific notation

Lesson
Worksheet
Practice
Worksheet
Scientific notation and calculators
1

Write the output on your calculator when you enter the following:

a
1.6 \times 10^{6}
b
1.8 \times 10^{ - 4 }
c
2.7 \times 10^{ - 2 }
d
3.32 \times 10^{ 5 }
e
7.45 \times 10^{ - 7 }
f
6.2 \times 10^{3}
g
4.35\times 10^{8}
h
8.16 \times 10^{ -5 }
2

Write the following in scientific notation:

a
254
b
0.0019
c
7870
d
0.000\,314
e
0.000\,009\,3
f
12\,345
g
5\,600\,000\,000
h
0.000\,017
3

Find the value of the following in scientific notation:

a
82.97 \times 7.1 \times 10^{4}
b
81\,000^{2} \times 4\,100\,000
c
3.808 \times 10^{15} \div \left( 5.6 \times 10^{8} \right)
d
\left( 8.3 \times 10^{10}\right) \times \left( 7.9 \times 10^{6}\right)
e
96.2 \times 10^{6} \div \left( 2.6 \times 10^{10}\right)
f
\left( 9.70 \times 10^{ - 2 }\right)^{3}
g
8.6 \times 10^{4} + 9.9 \times 10^{7}
h
\sqrt{ 2.89 \times 10^{ - 10 }}
i
\left( 3.8 \times 10^{13}\right) \times \left( 1.5 \times 10^{ - 6 }\right)
j
\left( 46.5 \times 10^{31}\right) \div \left( 6.2 \times 10^{15}\right)
k
\dfrac{61.2 \times 10^{18}}{9 \times 10^{13}}
l
\left( 2.6 \times 10^{17}\right) \times \left( 5.5 \times 10^{12}\right)
m
\left( 9 \times 10^{14}\right) \times \left( 3.5 \times 10^{ - 3 }\right)
n
\dfrac{8 \times 10^{3}}{16 \times 10^{ - 4 }}
o
5 \times 10^{ - 3 } \times 8 \times 10^{9}
p
\dfrac{800\,000\,000 \times 630\,000}{70\,000\,000\,000}
4

Complete the following statements:

a
5 \times 10^{ - 2 } \times 10^{4} = 5 \times ⬚
b
7.8 \times 10^{3} \times 10^{⬚} = 7.8 \times 10^{-7}
c
10^{12} \times 10^{-4}\times 9.3 = 9.3 \times 10^{⬚}
d
⬚\times 10^{-5} = 3.24 \times 10^{-10} \times 10^{5}
e
10^{-3}\times ⬚ \times 2.89 = 2.89 \times 10^{-5} \times 10^{-6}
f
10^{6}\times 10^{-3}\times 6.82 = 10^{⬚} \times 6.82
g
4 \times 10^{9} = 2 \times 10^{6} \times ⬚
h
2 \times 10^{-4} \times ⬚ = 3 \times 4 \times 10^{-6}
Applications
8

A country’s land size is approximately 56\,000 \text{ km}^2 and its population is approximately 28 million people.

a

Express the number of square kilometres in scientific notation.

b

Express the population in scientific notation.

c

Hence determine the population density measured in people per square kilometres in scientific notation.

9

A light year is defined as the distance that light can travel in one year. It is measured to be 9\,460\,730\,000\,000\,000 \text{ m}.

a

Express a light year in metres using scientific notation.

b

Express a light year in kilometres using scientific notation.

c

Express a light year in centimetres using scientific notation.

10

The average mass of a grain of sand is 1.5 \times 10^{ - 5 } \text{ g}. Over several years, a beach goes through a natural process of weathering and loses approximately 3.8 \times 10^{13} grains of sand.

Determine the mass of sand that is lost over this time period in scientific notation.

11

The mass of a planet is approximately 6.1 \times 10^{21} \text{ kg} and the mass of its single moon is \\\ 2.7 \times 10^{18} \text{ kg}. Determine the combined mass of the planet and its moon in scientific notation.

12

Light can travel at a speed of 300\,000\,000 \text{ m/s}.

a

Determine how far it will travel in 1 minute in scientific notation.

b

Determine how far it will travel in 1 hour in scientific notation.

c

Determine how far it will travel in 1 day in scientific notation.

13

A nanometre (\text{nm}) is defined as being a billionth of a metre. This means that 1 \text{ nm} is 0.000\,000\,001 \text{ m}. The width of a piece of hair has an approximate size of 100\,000 \text{ nm}. How many would fit in a 3 \text{ cm} sample?

14
The distance from Perth to Sydney is 3935 \text{ km}.
a

Express this distance in millimetres.

b

Hence, express this distance in millimetres using scientific notation.

15

The distance between Earth and the sun is 0.000\,016\,08 light years

(1 \text{ light year } = 9.46 \times 10^{15} \text{ m}).

a

Find the distance between Earth and the sun in kilometres. Write your answer as a whole number.

b

The circumference of the earth is approximately 40\,075 \text{ km}. State the equivalent amount of laps one must travel around the Earth to travel from Earth to the sun. Round your answer to the nearest integer.

16

1\text{ AU} (Astronomical Unit) is the distance from Earth to the sun where 1\text{ AU}= 149\,597\,900 \text{ km}). It is approximately 0.62\text{ AU} from Earth to Mercury.

Find the distance from Earth to Mercury in centimetres.

17

The tiny tubes in our kidneys measure about 1.2 \times 10^{ - 5 } \text{ m} in diameter. Determine the diameter of the tubes in millimetres. Write your answer as a decimal.

18

A plane is travelling 600\,000 \text{ m/hour}.

a

Express this in scientific notation.

b

An asteroid is travelling approximately 6 \times 10^{8} \text{ m/hour}. How many times faster is the asteroid travelling than the plane? Express your answer as a basic numeral.

19

An insect has an average mass of 0.6 \text{ g}. During a plague, it was estimated that there were 100 million insects in a particular area. Find the total mass of insects in scientific notation.

20

If the nucleus of a particular atom were the size of a table tennis ball, it would have a mass of approximately nine million metric tons. A metric ton is 1000 \text{ kg}.

Find the mass of the nucleus in kilograms. Express your answer in scientific notation.

21

A certain seed weighs about 0.002 \text{ g}.

a

Write this number in scientific notation.

b

If left to spread, the seed could reproduce and grow to 1 \times 10^{12} seeds in a few months. Find the total weight of these seeds in scientific notation.

22

Two stars, Tindalos and Cykranosh, in neighbouring galaxies have masses of 7.3 \times 10^{50} \text{ kg} and 15.33 \times 10^{53} \text{ kg} respectively. How many times more massive is Cykranosh than Tindalos? Give your answer in scientific notation.

23

An estimated 1.9 \times 10^{7} people watched the final of the last World Cup, while an estimated 1.4 \times 10^{7} people watched the final of the World Cup four years before. On average, how many people watched the final of the World Cup the last two times it occurred?

24

The mass of Earth is 5.96 \times 10^{21} tons and the mass of Venus is 4.82 \times 10^{21} tons. Express the total mass of the two planets in scientific notation.

25

A countrys land size is approximately 52\,000 \text{ km}^2 and its population is approximately 26 million.

a

Express the population in scientific notation.

b

Hence determine the number of square kilometres per person. Write your answer in scientific notation.

26

The mass of a blue whale is approximately 1.9 \times 10^{3} greater than the mass of an adult human who weighs 80 \text{ kg}. Thus, find the approximate mass of the blue whale. Write your answer in scientific notation.

27

A satellite orbits Earth at a speed of approximately 4.5 \times 10^{4} \text{km/hour}. A particular satellite has been orbiting Earth for 5 \times 10^{4} hours. Find the approximate distance that the satellite has orbited in this time. Write your answer in scientific notation.

28

A micrometre (\text{µm}) is defined as being a millionth of a metre. This means that 1 \text{ µm} is 0.000001 \text{ m}. The size of a fog, mist or cloud water droplet is approximately 10 \text{µm}. How many would fit in a 3 \text{ cm} sample? Write your answer to the nearest whole unit.

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Outcomes

ACMNA210

Express numbers in scientific notation

ACMMG219

Investigate very small and very large time scales and intervals

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