Standard
Form
Revision
Powers: 23  2  2  2  8
5  5  5  25
2
2 is multiplied
by itself 3 times
On calculator: 23  2
Try these:
Answers:
65
x
y
3 8
54
36
7776 625
729
25
94
32 6561
104
10 000
Powers of 10
e.g.103 = 10 x 10 x 10 =1000
Powers of 10 are easy
3 zeros
Look at these sequences
Divide by 10



1000 100
10
1
1000
10
1
10
3
100
10
2
1
10
10
0
0.1
1
10
0.01
1
100
0.001
1
1000
1
101
1
102
1
103
103
102
101
100
101 102 103
From this we see that 100  1 101  0.1 102  0.01
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
5.58 x 108 is said to be in Standard Form
or
Scientific Notation
558 000 000 is said to be in Normal Form
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 = 630 000
Standard form
Ordinary Number
watch this
5 jumps
63.5
6.3 x 10
1
630.
6300.
2
3
63000.
4
630000.
5
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
Add zeros
as required
• Write the answer
0 0
2 4 5 0 0
Now try these:
1234
Write as ordinary numbers:
1.47 x 102
147
9.08 x 106
9080000
1.3 x 100
1.3
4 x 103
4000
4.88 x 101
48.8
Ordinary Number
watch this
Standard form
630 000 = 6.3 x 100 000 = 6.3 x 105
630000. 63000.0 6300.00
1
2
630. 000 63.0000
3
4
5 jumps
x 105
Therefore 630 000 = 6.3 x 105
6.3000 0
5
Example:
Method:
Write 2706 in standard form.
• Write the number
• Insert “new” decimal point
• Count jumps to position of “old” decimal point
Positive
power since
large number
2 7 0 6
123
= 2 7 0 6 x 10
3
Now try these:
Make
Put
in athe
decimal
number
“look”
point
to make
the
like standard
number
“look” like a
form between 1
number
and 10.
Write in standard form:
34560
1023.6
3.456 x 104 1.0236 x 103
12.8
4.6
1.28 x 101
4.6 x 100
230000
2.3 x 105
Numbers less than 1
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.
Notice the power is negative
2.03 x 10-3 = 2.03 x 0.001 = 0.00203
Standard form watch this
Ordinary Number
-3
2.03 x 10
.203
.0203 .00203 = 0.00203
1
2
3
3 jumps
x 10-3
Look again
at powers
of 10
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
Add zeros
as required
• Write the answer
That means
answerisstarts
Note:
When the power
negative the
1234 1.
with 0.----ordinary
number is always less than
Now try these:
Write as ordinary numbers:
1.47 x 10-2
0.0147
0 0 0
0 0 0 01 0 7
9.08 x 10-5 1.3 x 10-1 4 x 10-3
0.0000908
0.13
0.004
4.081 x 10-4
0.0004081
Ordinary Number
watch this
Standard form
0.00631 = 6.31 x 0.001 = 6.31 x 10-3
0.00631 0 0.0631 00 0.631 00 0 6.31
1
2
3
3 jumps
x 10-3
Therefore 630 000 = 6.31 x 10-3
Example:
Method:
Write 0.0027 in standard form.
• Write the number
• Insert “new” decimal point
• Count jumps to position of “old” decimal point
Negative
power since
tiny number
0
0
=2
0
2
7 x 10 -
7
3
Now try these:
Write in standard form:
0.3456
0.00102
3.456 x 10-1 1.02 x 10-3
123 Put in a decimal
Make
the the
point
to make
number
“look”
number
“look”
like a
like standard
number
between 1
form
and
10.
0.0128
0.000046
1.28 x 10-2
4.6 x 10-5
0.0000000023
2.3 x 10-9
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
=
EXP 1
2
260 000 000
check this is
correct
3.5 x 1012
3
3.5
Too large to
convert
5
12
=
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)
= 1.092 x 1015
Example 2: (2.484 x 107)
calculator display
1.092
15
(4.6 x 10-4) calculator display
= 5.4 x 1010
5.4
10
Note:
See
calculators
again
• 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--
Click button to end presentation
(-)
END