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Teaching of Standard Form
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Standard Form
Powers: 822223 255552
Revision
On calculator: 8 3 223 yx
2 is multiplied by itself 3 times
Try these: 65 54 36 25 94 104
Answers: 7776 625 729 32 6561 10 000
3210123 10101010101010
Look at these sequences
1000
1
100
1
10
11101001000
3210123
10
1
10
1
10
110101010
Powers of 10
Powers of 10 are easy e.g.103 = 10 x 10 x 10 =1000
3 zeros
001.001.01.01101001000
Divide by 10
From this we see that 1100 1.010 1 01.010 2
Working with big numbers
Scientists often have to work with big numbers.
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.
Example:
558 000 000 = 5.58 x 100 000 000 = 5.58 x 108
is said to be in Standard Form
or Scientific Notation
5.58 x 108
558 000 000 is said to be in Normal Form
Look at this number which is in Standard Form
6.3 x 105
exactly one digit before the point
the power is a positive or negative whole number
6.3 x 105 = 6.3 x 10 x 10 x 10 x 10 x 10
= 630 000
Standard form Ordinary Numberwatch this
6.3 63.
1
630.
2
6300.
3
63000.
4
630000.
5
x 105
5 jumps
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
2 4 500
00
Add zeros as required
1234Now 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 9080000 1.3 4000 48.8
Standard formOrdinary Number watch this
= 6.3 x 105= 6.3 x 100 000630 000
6.363.630.
2
6300.
3
63000.
4
630000.
1 5
x 105
5 jumps
00 000 00000 0 0 0 0
Therefore
630 000 = 6.3 x 105
Example: Write 2706 in standard form.
Method: • Write the number
• Insert “new” decimal point
• Count jumps to position of “old” decimal point2 7 0 6 123
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
= 2 7 0 6 x 10 3
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.
Numbers less than 1
Consider the number 2.03 x 10-3
This number is in standard form but is different from previous examples.
exactly one digit before the point
the power is a positive or negative whole number
Notice the power is negative
2.03 x 10-3 = 2.03 x 0.001 = 0.00203
Look again at powers
of 10
Standard form Ordinary Numberwatch this
2.03 x 10-3.203 .0203 .00203
x 10-3
3 jumps
1 2 3
= 0.00203
Example: Write 1.07 x 10-4 as an ordinary number.
Method: • Write the question
• List the digits without the point
• 4 jumps from position of “old” point
• Write the answer
1 0 700
00
Add zeros as required
1234
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 0.0000908 0.13 0.004 0.0004081
000
That means the answer starts with 0.-----
Note: When the power is negative the ordinary number is always less than 1.
Standard formOrdinary Number watch this
= 6.31 x 10-3= 6.31 x 0.0010.00631
6.31
2
0.631
3
0.06310.00631
1
x 10-3
3 jumps
0000 0 0
Therefore
630 000 = 6.31 x 10-3
Example: Write 0.0027 in standard form.
Method: • Write the number
• Insert “new” decimal point
• Count jumps to position of “old” decimal point
= 2 7
123
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
Put in a decimal point to make the number “look” like a number between 1 and 10.
0 0 0 2 7
x 10
Negative power since tiny number -
3
Make the number “look” like standard form
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 2 6 EXP 8 =
260 000 000check this is
correct
3.5 x 1012
3.5 12
3 5 EXP 1 2 =
Too large to convert
Calculator’s way of writing 3.5 x 1012 – does not mean 3.5 to the power 12!
Calculations Giving your Answer in Standard Form
Example 1: (2.6 x 108) x (4.2 x 106) calculator display
1.092 15= 1.092 x 1015
Example 2: calculator display
5.4 10= 5.4 x 1010
(2.484 x 107) (4.6 x 10-
4)
Note:
• Only enter EXP before power, never x 10 EXP
• For negative powers use the ( - ) key not the key, we are not subtracting.
• Remember to change number on display to ---- x 10--
See calculators
again
Click button to end presentation
( - )
END