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.
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