Indices, Standard Form And Surds Worksheet Page 6

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25.2 Using standard form
Method 2
a
40  10
2
 40  100
 4000
Work out the calculation.
 4  10
3
Change the answer into standard form.
___
1
0.008  10
 0.008 
b
2
100
 0.008  100
__
1
a
n
Use the rule
.
a
n
 0.000 08
___
1
Multiplying by
is the same as dividing by 100.
100
 8  10
5
Exercise 25D
B
Write these in standard form.
1
a
45  10
3
b
980  10
c
3400  10
d
186  10
10
3
2
Write these in standard form.
2
a
0.009  10
5
b
0.045  10
6
c
0.3708  10
d
0.006  10
12
7
Some of these numbers are not in standard form. If a number is in standard form then say so.
3
If a number is not in standard form then rewrite it so that it is in standard form.
4
6
9
a
7.8  10
b
890  10
c
13.2  10
5
d
0.56  10
8
15
e
60 000  10
f
8.901  10
7
g
0.040 05  10
10
h
9080  10
5
8
3
6.002  10
0.0046  10
67 000  10
3
0.004  10
i
j
k
l
Write these numbers in order of size. Start with the smallest number.
4
6.3  10
6
, 0.637  10
7
, 6290000, 63.4  10
5
Write these numbers in order of size. Start with the smallest number.
5
0.034  10
, 3.35  10
, 0.000033, 37  10
2
5
4
Example 7
Work out (3  10
)  (4  10
) giving your answer in standard form.
6
3
Rearrange the expression so the powers of 10 are
(3  10
6
)  (4  10
3
)  3  4  10
6
 10
3
.
together
 12  10
9
Multiply the numbers.
 1.2  10
1
 10
9
a
m
a
n
a
m
n
Use
to multiply the powers of 10.
9
12  10
is not in standard form.
 1.2  10
10
Write your fi nal answer in standard form.
Example 8
By writing 760 000 000 and 0.000 19 in standard form correct to one signifi cant fi gure, work
out an approximation for 760 000 000  0.000 19.
760 000 000  8  10
8
correct to one signifi cant fi gure.
0.000 19  2  10
correct to one signifi cant fi gure.
4
760 000 000
 8  10
8
_____________
_________
0.000 19
2  10
4
Rearrange the expression so the powers of 10
 10
8
 8
__
_____
are together.
2
10
4
Divide the numbers.
 4  10
84
a
m
a
n
a
m
n
Use
to divide the powers of 10.
 4  10
12
615

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