Topics
1 The real numbers
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Australia
Year 9

1.03 Introducing scientific notation

Lesson
Worksheet
Practice
Worksheet
Scientific notation
1

Express the following numbers as basic numerals:

a
2 \times 10^{7}
b
4.13 \times 10^{4}
c
9 \times 10^{ - 3 }
d
8.97 \times 10^{5}
e
5.03 \times 10^{5}
f
3.014 \times 10^{3}
g
8 \times 10^{ 6 }
h
1.3008 \times 10^{7}
2

Express the following numbers in scientific notation:

a
45
b
128
c
2000
d
884\,000
e
84\,626\,000
f
23\,456
g
6.14
h
9\,700\,000\,000
3

Express the following numbers in scientific notation:

a
0.6
b
0.002
c
0.000\,74
d
\dfrac{1}{10\,000}
e
0.000\,347
f
\dfrac{3}{100\,000}
g
0.000\,059\,32
h
\dfrac{92}{1000}
4

Express the following numbers as decimals:

a
8.29 \times 10^{0}
b
7 \times 10^{ - 3 }
c
5.28 \times 10^{ - 2 }
d
4.7 \times 10^{ - 6 }
e
2.13 \times 10^{ - 7 }
f
3.62 \times 10^{ - 4 }
g
6.4 \times 10^{ - 5 }
h
9.72 \times 10^{ - 2 }
5

Complete the following statements:

a
0.002 = ⬚ \times 10^{ - 3 }
b
⬚ = 7.3 \times 10^{ -4}
c
89\,300\,000 = 8.93 \times 10^{ ⬚}
d
4000 = ⬚ \times 10^{3}
e
⬚ = 7.34 \times 10^{5}
f
0.000\,067 = 6.7 \times 10^{ ⬚}
6

State whether the following are written in scientific notation:

a
8.56 \times 10^{14}
b
0.658 \times 10^{3}
c
608.56 \times 10^{14}
d
465.53 \times 10^{21}
7

For each of the following set of numbers:

i

State the largest number.

ii

State the smallest number.

a

  • 7.27 \times 10^{ - 7 }

  • 2.22 \times 10^{ - 7 }

  • 4.76 \times 10^{ - 7 }

b
  • 7.31 \times 10^{ - 9 }
  • 5.13 \times 10^{ - 9 }
  • 8.31 \times 10^{ - 9 }
c
  • 1.25 \times 10^{ - 2 }
  • 1.25 \times 10^{ - 6 }
  • 1.25 \times 10^{2}
d
  • 9.37 \times 10^{ - 4 }
  • 6 \times 10^{ - 4 }
  • 6 \times 10^{ - 9 }
e
  • 2.93 \times 10^{ - 2 }
  • 7.88 \times 10^{2}
  • 7.88 \times 10^{ - 2 }
f
  • 4.7 \times 10^{2} \times 10^{3}
  • 4.7 \times 10^{ - 8 } \times 10^{8}
  • 4.7 \times 10^{9} \times 10^{8}
8

Use index laws to simplify the following in scientific notation:

a
2\times 10^6\times 6\times 10^5
b
4\times10^{-3}\times4\times10^{-5}
c
\dfrac{15\times 10^6}{ 5\times 10^3}
d
\dfrac{9\times10^{-3}}{3\times10^{-5}}
Applications
9

The thickness of coating on a camera lens is 0.000\,002 metres. Express the thickness in scientific notation.

10

The distance between two stars is approximate 5 \times 10^{6} metres. Express this distance as a whole number.

11

The world's oceans hold approximately 188\,000\,000\,000\,000\,000\,000 gallons of water. Express this volume of water in scientific notation.

12

Bone marrow in a person’s body produces 2.3 \times 10^{6} red blood cells each second.

a

Express the amount of red blood cells as a whole number.

b

Determine the number of red blood cells produced each minute. Express your answer in scientific notation.

13

Sound travels at a speed of approximately 0.3 kilometres per second, while light travels at a speed of approximately 300\,000 kilometres per second.

a
Express the speed of sound in kilometres per second in scientific notation.
b
Express the speed of light in kilometres per second in scientific notation.
c
How many times faster does light travel than sound?
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Outcomes

ACMNA209

Apply index laws to numerical expressions with integer indices

ACMNA210

Express numbers in scientific notation

ACMNA212

Extend and apply the index laws to variables, using positive integer indices and the zero index

ACMMG219

Investigate very small and very large time scales and intervals

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