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
84
a
m
a
n
a
m
n
Use
to divide the powers of 10.
4 10
12
615