1. Standard Form

2. Revision
Powers:
2 is multiplied by itself 3 times
On calculator:
Try these: 65 54 36 25 94
104
Answers:
10 000
7776
625
729 32
6561

3. Powers of 10 Powers of 10 are easy e.g.103 = 10 x 10 x 10 =1000
3 zeros
Look at these sequences
Divide by 10
From this we see that

4. Working with big numbers
Scientists often have to work with big numbers.
Example:
The distance the earth travels in one orbit is miles.
We can express this number in a more concise form as follows.
= 5.58 x = 5.58 x 108
5.58 x 108
is said to be in
Standard Form or
Scientific Notation
is said to be in
Normal Form

5. Look at this number which is in Standard Form
6.3 x 105
the power is a positive or negative whole number
exactly one digit before the point
6.3 x 105
= 6.3 x 10 x 10 x 10 x 10 x 10 =
watch this
Standard form
Ordinary Number
x 105
5 jumps
6.3
63. 1
630. 2
6300. 3
63000. 4 5

6. Example:
Write 2.45 x 104 as an ordinary number.
Method:
Write the question
List the digits without the point
4 jumps from position of “old” point
Write the answer
Add zeros as required 2 1 3 4
Now try these:
Write as ordinary numbers:
1.47 x 102
9.08 x 106
1.3 x 100
4 x 103
4.88 x 101
147
1.3
4000
48.8

7. Ordinary Number Standard form watch this 630 000 = 6.3 x 100 000
63000.
6300.
630.
63.
6.3 1 2 4 5 3
x 105
5 jumps
Therefore
= 6.3 x 105

8. Positive power since large number
Example:
Write 2706 in standard form.
Method:
Write the number
Insert “new” decimal point
Count jumps to position of “old” decimal point
Positive power since large number
Make the number “look” like standard form
Put in a decimal point to make the number “look” like a number between 1 and 10. 3 1 2 = x 10 3
Now try these:
Write in standard form:
34560
1023.6
12.8
4.6
230000
3.456 x 104
x 103
1.28 x 101
4.6 x 100
2.3 x 105

9. Numbers less than 1 Standard form Ordinary Number Consider the number
2.03 x 10-3
exactly one digit before the point
the power is a positive or negative whole number
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 =
watch this
Standard form
Ordinary Number
x 10-3
3 jumps
2.03
x 10-3
.203
.0203
.00203 = 1 2 3

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
Note: When the power is negative the ordinary number is always less than 1.
That means the answer starts with 2 3 1 4
Now try these:
Write as ordinary numbers:
1.47 x 10-2
9.08 x 10-5
1.3 x 10-1
4 x 10-3
4.081 x 10-4
0.0147
0.13
0.004

11. Ordinary Number Standard form watch this 0.00631 = 6.31 x 0.001
0.0631
0.631
6.31 1 2 3
x 10-3
3 jumps
Therefore
= 6.31 x 10-3

12. Negative power since tiny number
Example:
Write in standard form.
Method:
Write the number
Insert “new” decimal point
Count jumps to position of “old” decimal point
Negative power since tiny number
Put in a decimal point to make the number “look” like a number between 1 and 10. 3 1 2
Make the number “look” like standard form 3 = x 10 -
Now try these:
Write in standard form:
0.3456
0.0128
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

13. Standard Form on the Calculator
We use EXP button as shown on the calculator to enter numbers already in standard form.
Examples:
2.6 x 108
EXP =
check this is correct
3.5 x 1012
EXP =
Calculator’s way of writing 3.5 x 1012 – does not mean 3.5 to the power 12!
Too large to convert

14. Calculations Giving your Answer in Standard Form
calculator display
Example 1:
(2.6 x 108) x (4.2 x 106)
= x 1015
calculator display
Example 2:
(2.484 x 107) (4.6 x 10-4)
= 5.4 x 1010
Note:
Only enter EXP before power, never x EXP
See calculators again
For negative powers use the ( - ) key not the key, we are not subtracting.
Remember to change number on display to x 10--
Click button to end presentation

15. ( - )

16. END