Indices, Standard Form And Surds Worksheet Page 3
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17Chapter 25 Indices, standard form and surds
Exercise 25A
Questions in this chapter are targeted at the grades indicated.
B
Write down the value of these expressions.
1
a
7
0
b
8
c
5
d
4
0
1
1
e
(2)
f
9
g
10
h
145
0
3
2
4
i
(3)
j
(8)
0
k
16
0
l
10
2
6
Work out the value of these expressions.
2
(
_
)
(
_
)
(
_
)
(
_
)
1
2
1
1
a
1
b
1
c
2
d
3
7
7
4
3
(
)
(
)
(
)
_
_
_
2
5
0
9
e
(0.25)
f
3
g
h
1
2
5
3
5
(
)
(
)
_
_
2
1
i
1
2
j
1
3
k
(0.1)
l
(0.2)
4
3
5
3
25.2
Using standard form
Why do this?
Objectives
Astronomers use standard form to record large
You can convert ordinary numbers into standard form.
measurements. The Sun’s diameter is about
You can convert numbers in standard form into
1.392 10
km. Biologists working with micro-
6
ordinary numbers.
organisms sometimes use standard form to
You can calculate with numbers in standard form
record their very small sizes, like 2.1 10
cm.
You can convert to standard form to make sensible
4
estimates for calculations.
Get Ready
1. Work out
a 10
b 10
3
–2
2. Write 10 000 as a power of 10.
3. Work out 2.35 10 000.
Key Points
Standard form is used to represent very large (or very small) numbers.
A number is in standard form when it is in the form a 10
where 1 a 10 and n is an integer.
n
To use standard form you need to know how to write powers of ten in index form.
10
1
10
100 10 10
10
2
1000 10 10 10 10
3
A number in standard form looks like this.
6.7 10
4
This part is written as a
This part is written as a
number between 1 and 10.
power of 10.
These numbers are all in standard form – 4.5 10
2
, 9 10
, 1.2657 10
6
.
8
These numbers are not in standard form – 67 10
9
, 0.087 10
3
– because the fi rst number is not between
1 and 10.
It is often easier to multiply and divide very large or very small numbers, or estimate a calculation if the numbers
are written in standard form.
To input numbers in standard form into your calculator, use the 10 or EXP key.
·
To enter 4.5 10
7
press the keys 4
7 .
5 � 10
612
standard form
integer
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