Indices, Standard Form And Surds Worksheet Page 7

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Chapter 25 Indices, standard form and surds
Exercise 25E
A
Work out and give your answer in standard form.
1
a
(4  10
8
)  (2  10
3
)
b
(6  10
5
)  (1.5  10
3
)
c
(4  10
)  (3  10
5
)
7
d
(6  10
7
)  (3  10
)
e
(6  10
9
)  (5  10
3
)
f
(5  10
)  (2  10
3
)
6
8
Work out and give your answer in standard form.
2
a
(4  10
8
)  (2  10
3
)
b
(9  10
5
)  (2  10
)
c
(3  10
)  (6  10
3
)
4
9
d
(8.6  10
8
)  (2  10
13
)
e
(1  10
12
)  (4  10
3
)
f
(7  10
)  (7  10
)
9
5
Express in standard form.
3
(2  10
)
(5  10
)
(4  10
)
(7  10
)
a
5
2
b
2
c
6
2
d
2
5
8
By writing these numbers in standard form correct to one signifi cant fi gure, work out an estimate of the
4
value of these expressions. Give your answer in standard form.
a
600 008  598
b
78 018  4180
c
699 008  198
d
8 104 660 000  0.000 078
Light travels at 3  10
metres per second.
8
5
Work out the time it takes light to travel:
a
200 metres
b
1.5 centimetres.
The base of a microchip is in the shape of a rectangle. Its length is 2  10
3
mm and its width is
6
1.6  10
mm. Find the area of the base. Give your answer in mm
2
in standard form.
3
The distance of the Earth from the Sun is approximately 93 000 000 miles.
7
AO 3
Light travels at a speed of approximately 300 000 kilometres per second.
Work out an estimate of the time it takes light to travel from the Sun to the Earth.
An atomic particle has a lifetime of 3.86  10
seconds. It travels at a speed of 4.2  10
metres per
6
8
5
AO 2
A O 3
second. Calculate an approximation for the distance it travels in its lifetime.
Example 9
Use a calculator to work out
a
(3.4  10
6
)  (7.1  10
4
)
b
(4.56  10
8
)  (3.2  10
)
3
x
6
4
11
a
(3.4  10
)  (7.1  10
)
 2.414  10
Use the EXP of 10
on your calculator.
8
11
b
(4.56  10
)  (3.2  10
)  1.425  10
3
Hint
Hint
In both of these cases the
brackets need not be used, but
in more complex expressions the
brackets must be used.
616

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