Standard Form

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Standard Form
2
Revision
Powers
On calculator
Try these
65
54
36
25
94
104
10 000
Answers
7776
625
729
32
6561
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Powers of 10
Powers of 10 are easy
e.g.103 10 x 10 x 10 1000
Look at these sequences
Divide by 10
From this we see that
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Working with big numbers
Scientists often have to work with big numbers.
Example
The distance the earth travels in one orbit
is 558 000 000 miles. We can express
this number in a more concise form as follows.
558 000 000 5.58 x 100 000 000 5.58 x 108
is said to be in
Standard Form
5.58 x 108
or
Scientific Notation
558 000 000
is said to be in
Normal Form
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Look at this number which is in Standard Form
6.3 x 105
6.3 x 105
6.3 x 10 x 10 x 10 x 10 x 10
630 000
Standard form
Ordinary Number
6.3
6
Example
Write 2.45 x 104 as an ordinary number.

• Write the question
• List the digits without the point
• 4 jumps from position of old point
• Write the answer

Method
Add zeros as required
0
0
2 4 5
0
0
1
3
4
2
Now try these
Write as ordinary numbers
4 x 103
4.88 x 101
1.47 x 102
9.08 x 106
1.3 x 100
147
9080000
1.3
4000
48.8
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Ordinary Number
Standard form
6.3 x 105
6.3 x 100 000
630 000
63000.
6300.
630000.
0
0
0
6.3
630.
0
0
0
0
0
0
0
0
0
0
0
63.
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Example
Write 2706 in standard form.
Method

• Write the number
• Insert new decimal point
• Count jumps to position of old decimal point

2 7 0 6
2
3
1
x
3
10
Now try these
Write in standard form
34560
1023.6
12.8
4.6
230000
3.456 x 104
1.0236 x 103
1.28 x 101
4.6 x 100
2.3 x 105
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Numbers less than 1
Consider the number
2.03 x 10-3
This number is in standard form but is different
from previous examples.
Look again at powers of 10
Notice the power is negative
2.03 x 10-3
2.03 x 0.001
0.00203
Standard form
Ordinary Number
2.03
x 10-3
.203
.0203
.00203
0.00203
10
Example
Write 1.07 x 10-4 as an ordinary number.

• Write the question
• List the digits without the point
• 4 jumps from position of old point
• Write the answer

Method
Add zeros as required
That means the answer starts with 0.-----
Note When the power is negative the ordinary
number is always less than 1.
0
0
0
1
3
4
2
0
1 0 7
0
0
0
Now try these
Write as ordinary numbers
4 x 10-3
4.081 x 10-4
1.47 x 10-2
9.08 x 10-5
1.3 x 10-1
0.0147
0.0000908
0.13
0.004
0.0004081
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Ordinary Number
Standard form
6.31 x 10-3
6.31 x 0.001
0.00631
0.631
0.00631
0
0
0
0.0631
6.31
0
0
0
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Example
Write 0.0027 in standard form.
Method

• Write the number
• Insert new decimal point
• Count jumps to position of old decimal point

2
3
1
3
x
10
-
Now try these
Write in standard form
0.3456
0.00102
0.0128
0.000046
0.0000000023
3.456 x 10-1
1.02 x 10-3
1.28 x 10-2
4.6 x 10-5
2.3 x 10-9
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Standard Form on the Calculator
Examples
2.6 x 108
260 000 000
3.5 x 1012
Calculators way of writing 3.5 x 1012 does not
mean 3.5 to the power 12!
3.5 12
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Calculations Giving your Answer in Standard Form
Example 1
(2.6 x 108) x (4.2 x 106)
1.092 x 1015
1.092 15
Example 2
5.4 x 1010
5.4 10
Note
See calculators again

• Remember to change number on display to ---- x
  10--

Click button to end presentation
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END