Factors, Powers And Standard Form Worksheet Page 9
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21C
14
Estimate the answers to these calculations by rounding each value to the nearest
whole number.
__________
_________
3
√
a
b
c
d
6.7
2
1 3.1
2
5.04
3
2 3.28
3
√
19.8 2 4.1
2.1
2
1 1.7
2
C
15
Amber and Simon have each made a 10 cm square pattern using 1 cm square tiles.
Amber gives some tiles to Simon. They are both able to arrange their tiles exactly
into square patterns.
How many tiles did Amber give to Simon?
3
AO
10.4
Indices
Keywords
index notation,
Why learn this
Objectives
index, indices,
The formula for radioactive
E
Understand and use index notation
base, power
decay uses indices.
in calculations
Scientists use this formula
B
Understand and use negative powers and numbers to
to work out the age of
the power of 1 or 0
fossils.
Skills check
1 Work out
a 3 3 3 3 3
b 2 3 2 3 2 3 2
c 8 3 8
d 5 3 5 3 5 3 5
2 Work out
__
a 6 3 6 3 6
c 2 3 2 3 2 3 2 3 2
_________
_________________
b
√
3
4
6
2 3 2 3 2
Positive and negative indices
You can write numbers using index notation.
This number is called the index.
The plural of index is indices.
2 3 2 3 2 3 2 3 2 3 2 5 2
6
6
. You say ‘two to the power of six’ .
You write 2
This number is called the base.
This sequence of numbers halves each time.
5
2
5 2 3 2 3 2 3 2 3 2 5 32
2
4
5 2 3 2 3 2 3 2 5 16
2
3
5 2 3 2 3 2 5 8
2
2
5 2 3 2 5 4
The next power in this sequence is 2
1
. You can continue the pattern by halving.
2
1
5 2
Any number to the power of 1 is the number itself.
2
0
5 1
Any number to the power of 0 is equal to 1.
_
1
2
21
5
2
__
__
1
1
You can write 2
as
and 2
as
.
_
2
3
1
2
22
5
2
2
2
3
4
If the index is negative, fi rst change it to positive.
_
1
2
23
5
Then write the number as the denominator of a fraction.
8
166
Factors, powers and standard form
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