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Stage 5.1-2

1.03 Introducing scientific notation

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

MA5.1-9MG

interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures

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