Standard Form. 2 is multiplied by itself 3 times. Revision. Powers:. On calculator:. Try these:. 6 5. 5 4. 3 6. 2 5. 9 4. 10 4. 10 000. Answers:. 7776. 625. 729. 32. 6561. 3 zeros. Powers of 10. Powers of 10 are easy. e.g.10 3 = 10 x 10 x 10 =1000.
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Standard Form
2 is multiplied by itself 3 times
Revision
Powers:
On calculator:
Try these:
65
54
36
25
94
104
10 000
Answers:
7776
625
729
32
6561
3 zeros
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
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
is said to be in
Normal Form
558 000 000
the power is a positive or negative whole number
exactly one digit before the point
watch this
5 jumps
63.
x 105
630.
6300.
630000.
63000.
2
1
3
4
5
Look at this number which is in Standard Form
6.3 x 105
6.3 x 105
= 630 000
= 6.3 x 10 x 10 x 10 x 10 x 10
Standard form
Ordinary Number
6.3
Example:
Write 2.45 x 104 as an ordinary number.
Method:
Add zeros as required
0
0
0
0
2 4 5
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
4
1
5
3
2
watch this
5 jumps
Therefore
630 000
= 6.3 x 105
x 105
Ordinary Number
Standard form
630 000
= 6.3 x 100 000
= 6.3 x 105
63000.
630000.
0
0
0
6300.
0
0
0
0
0
0
0
0
0
0
0
630.
6.3
63.
Make the number “look” like standard form
Positive power since large number
Put in a decimal point to make the number “look” like a number between 1 and 10.
= 2 7 0 6
Example:
Write 2706 in standard form.
Method:
2 7 0 6
3
2
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
the power is a positive or negative whole number
exactly one digit before the point
watch this
3 jumps
x 103
1
2
3
Numbers less than 1
Consider the number
2.03 x 103
This number is in standard form but is different from previous examples.
Look again at powers of 10
Notice the power is negative
= 0.00203
2.03 x 103
= 2.03 x 0.001
Standard form
Ordinary Number
x 103
2.03
.203
.0203
.00203
= 0.00203
Example:
Write 1.07 x 104 as an ordinary number.
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:
4.081 x 104
4 x 103
1.47 x 102
9.08 x 105
1.3 x 101
0.0147
0.0000908
0.13
0.004
0.0004081
1
3
2
watch this
3 jumps
Therefore
630 000
= 6.31 x 103
x 103
Ordinary Number
Standard form
0.00631
= 6.31 x 0.001
= 6.31 x 103
0.00631
0
0
0
0.631
0.0631
0
0
0
6.31
Make the number “look” like standard form
0 0 0 2 7
Negative power since tiny number
Put in a decimal point to make the number “look” like a number between 1 and 10.
= 2 7
Example:
Write 0.0027 in standard form.
Method:
3
2
1
3
x
10

Now try these:
Write in standard form:
0.3456
0.00102
0.0128
0.000046
0.0000000023
3.456 x 101
1.02 x 103
1.28 x 102
4.6 x 105
2.3 x 109
We use EXP button as shown on the calculator to enter numbers already in standard form.
2 6 EXP 8 =
check this is correct
Too large to convert
3 5 EXP 1 2 =
Standard Form on the Calculator
Examples:
2.6 x 108
260 000 000
3.5 x 1012
Calculator’s way of writing 3.5 x 1012 – does not mean 3.5 to the power 12!
3.5 12
calculator display
calculator display
(2.484 x 107) (4.6 x 104)
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
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