Transcript Standard Index form
Slide 1
Standard Index form
Objective:
To convert numbers into
standard index form
Slide 2
Why is this number very difficult to use?
999,999,999,999,999,999,999,999,999
Too big to read
Too large to comprehend
Too large for calculator
To get around using numbers this large, we
use standard index form.
Slide 3
Reminder About Powers of 10
10 = 101
100 = 10 X 10 = 102
1000 = 10 X 10 X 10 = 103
10000 = 10 X 10 X 10 X 10 = 104
100000 = 10 X 10 X 10 X 10 X 10 = 105
Rule: Count the number of zeros
Slide 4
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
This means 2 in the hundreds so its worth 200
This means 3 in the tens so its worth 20
This means 5 in the units so its worth 5
This means 7 in the tenths so its worth
7
10
This means 1 in the hundreds so its worth
9
or 1.7
000
1
100
This means 9 in the thousandths so its worth
or .01
or .009
Slide 5
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
5
3
7
9
2
1
If you multiply by 10 all the digits move 1 place to the
left.
200 becomes 2000
30 becomes
300
5 becomes
50
So 235.719 X 10 =
2 3 5 .7 1 9
Slide 6
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
If you multiply by 100 all the digits move 2 places to the
left.
200 becomes 20000
30 becomes
3000
5 becomes
500
So 235.719 X 100 =
2 3 5.7 1 9
Slide 7
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
If you divide by 10 all the digits move 1 place to the
right.
200 becomes 20
30 becomes
3
5 becomes
5
.
So 235.719 10 =
2 3 5.7 1 9
Slide 8
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
If you divide by 100 all the digits move 2 places to the
right.
200 becomes 2
30 becomes 3
5 becomes 05
.
.
So 235.719 100 =
2 3 5 .7 1 9
Slide 9
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
Instead of moving the digits most people think it easier
to move the point
.
235.719 x 10 = 2 3 5 7 1 9
.
235.719 x 100 = 2 3 5 7 1 9
.
235.719 100 = 2 3 5.7 1 9
235.719 10 = 2 3 5 7 1 9
But it is actually the
digits that move
Slide 10
Let’s investigate!
Converting large numbers
How could we turn the number 800,000,000,000 into
standard index form?
We can break numbers into parts to make it easier,
e.g. 80 = 8 x 10 and 800 = 8 x 100
800,000,000,000 = 8 x 100,000,000,000
And 100, 000,000,000 = 1011
So, 800,000,000,000 = 8 x 1011 in standard index form
Slide 11
Try it out!
How can we convert 30,000 into standard index
form?
Break into easier parts:
30000 = 3 x 10,000
And, 10,000 = 104
So 30,000 = 3 x 104 in standard index
form
The number is now easier to use
Slide 12
Now it’s your turn:
Copy down the following numbers, and convert them
into standard index form.
a) 500
= 5 x 100 = 5 x 102
b) 4000 = 4 x 1000 = 4 x 103
4
=
6
x
10,000
=
6
x
10
c) 60,000
d) 900,000 = 9 x 100,000 = 9 x 105
e) 7000,000 = 7 x 1000,000 = 7 x 106
Slide 13
One of the most important rules for writing
numbers in standard index form is:
The first number must be a value between
1 and 9
For example, 39 x 106 does have a value but it’s
not written in standard index form.
The first number, 39, is greater than 10.
But 39 = 3.9 x 10
So 39 x 106 = 3.9 x 10 x 106
Add powers
= 3.9 x 107
Slide 14
How could we convert 350,000,000 into
standard index form?
Again, we can break the number into smaller, more
manageable parts.
350,000,000 = 3.5 x 100,000,000
100,000,000 = 108
350,000,000 = 3.5 x 108 in standard index form
Slide 15
Try it out!
How can we convert 67,000 into
standard index form?
67,000 = 6.7 x 10,000
10,000 = 104
67,000 = 6.7 x 104 in standard index form
Slide 16
Now it’s your turn:
Copy out the following numbers and convert
them into standard index form.
a) 940
= 9.4 x 100 = 9.4 x 102
b) 8,600
= 8.6 x 1000 = 8.6 x 103
c) 34, 000
= 3.4 x 10,000 = 3.4 x 104
d) 570,000
= 5.7 x 100,000 = 5.7 x 105
e) 1,200,000
= 1.2 x 1000,000 = 1.2 x 106
Slide 17
Can you find a quick method of converting
numbers to standard form?
For example,
Converting 45,000,000,000 to standard form
Place a decimal point after the first digit
4.5000000000
10
Count the number of digits
after the decimal point.
This is our index number (our power of 10)
So, 45,000,000,000 = 4.5 x 1010
Slide 18
Using the quick method
Example 237000000
Place the decimal point between the 2
and 3 (2.37000000)
Then count the number of places that the
decimal point has moved.
237000000 = 2.37 x 108
8 places
Slide 19
Reminder about Negative
Powers
0.1=
1
10
10–1
1
0.01 =
100
1
0.001 =
0.0001=
1000
10–2
10–3
1
10000
10–4
Slide 20
Converting Very Small Numbers
into Standard Form
0.23 is not in standard form as the 1st digit is
NOT between the 1 and 9
But 0.23 =
2 .3
10
Remember to divide by 10
move the digits right
Using the rules of powers
So 0.23 =
2 .3
10
1
10
= 2.3 x 10–1
10–1
Slide 21
Converting Very Small Numbers
into Standard Form
0.056 is not in standard form as the 1st digit is
NOT between 1 and 9
But 0.056 =
5 .6
100
Remember to divide by 100
move the digits 2 places right
Using the rules of powers
So 0.056 =
5 .6
100
1
100
= 5.6 x 10–2
10–2
Slide 22
Converting Very Small Numbers
into Standard Form
0.00039 is not in standard form as the 1st digit is
NOT between 1 and 9
3 .9
Remember to divide by 10000
1 0 0 0 0 move the digits 4 places right
But 0.00039 =
Using the rules of powers
So 0.00039 =
3 .9
10000
1
10000
10–4
= 3.9 x 10–4
Slide 23
Now it’s your turn:
Copy out the following numbers and convert
them into standard index form.
a) 0.94
b) 0.086
= 9.4 10 = 9.4 x 10–1
= 8.6 100 = 8.6 x 10–2
c) 0.00034 = 3.4 10000 = 3.4 x 10–4
d) 0.0057
e) 0.000012
= 5.7 1000 = 5.7 x 10–3
= 1.2 100000 = 1.2 x 10–5
Slide 24
Converting to Normal Numbers
Slide 25
To convert standard form to ordinary
numbers: Positive powers
1.31 x 105
Write the digits 1 31
Hundreds
Tens
Remember 105 means
multiply by 10000
Units
Tenths
Hundredths
1
3
1
Thousandths
Now move all the digits 5 places left
But this is the same as moving the decimal point 5
places right
Slide 26
To convert standard form to ordinary
numbers: Positive powers
1.31 x 105
Write the digits 1 31
Hundreds
Tens
Units
Tenths
Hundredths
1
3
1
Which ever way you think about it the
number gets BIGGER
1.310000=
131000
1.310000= 1 3 1 0 0 0
Thousandths
Slide 27
To convert standard form to ordinary
numbers: Negative powers
1.31 x
10–2
Remember
Write the digits 1 31
Hundreds
Tens
10–2
means
1
10
2
1
100
So DIVIDE by 100
Units
Tenths
Hundredths
1
3
1
Thousandths
Now move all the digits 2 places right
But this is the same as moving the decimal point 2
places left
Slide 28
To convert standard form to ordinary
numbers: Negative powers
1.31 x
10–2
Remember
10–2
means
10
Write the digits 1 31
Hundreds
Tens
Units
Tenths
Hundredths
1
3
1
Which ever way you think about it the
number gets Smaller
01.31= 0 1 3 1
1.31= 0 1 3 1
1
2
1
100
Thousandths
Slide 29
The ordinary number is:
So if the power is positive, the
ordinary number is BIG
If the power number is negative the
ordinary number is small
Slide 30
Multiplying standard form
1.27 x 105 x 2.36 x 104
Separate the calculation into 2 parts as
follows:
(1.27 x 2.36) x (105 x 104)
= 2.9972
X
109
Rule of index
says we ADD the
powers!
Slide 31
Sometimes when we multiply out
the first part we can get more
than one digit before the decimal
point.
23.742 x 106
This can be rewritten as
Rule of
2.3742 x 10 x 106 indices
says we
which becomes
ADD
powers
2.3742 x 107
Slide 32
Division of Standard Form
If when we multiply standard form, we
add the powers, when we divide standard
form we-----
Subtract the powers
Slide 33
Division in Standard Form
4.8 x 107 ÷ 1.5 x 103
Separate into two parts
(4.8 ÷ 1.5)
x
3.2
x
(107 ÷ 103)
3.2 x 104
10(7-3)
Rule of
indices says
subtract the
powers!!
Slide 34
Sometimes we get a number that has a zero
before the decimal point….
0.742 x 1012
This can be rewritten as:
7.42 x 10-1 x 1012
7.42 x 1011
Rule of
indices
says ADD
the
powers
Slide 35
Standard Form
These are numbers of the type
a x 10n
Where a is a decimal number with only one digit in front (left) of the decimal point
n is a whole number that can be positive or negative
How can we convert 30,000 into standard index form?
Break into easier parts:
30000 = 3 x 10,000
And, 10,000 = 104
So 30,000 = 3 x 104 in standard index form
a)
500 = 5 x 100 = 5 x 102
b)
4000 = 4 x 1000 = 4 x 103
c)
60,000 = 6 x 10,000 = 6 x 104
d)
900,000 = 9 x 100,000 = 9 x 105
e)
7000,000 = 7 x 1000,000 = 7 x 106
Slide 36
One of the most important rules for writing numbers in standard index form is
The first number must be a value between 1 and 9
For example, 39 x 106 does have a value but it’s not written in standard index form.
The first number, 39, is greater than 10.
But 39 = 3.9 x 10
So 39 x 106 = 3.9 x 10 x 106 = 3.9 x 107
a)
940 = 9.4 x 100 = 9.4 x 102
b)
8,600= 8.6 x 1000 = 8.6 x 103
c)
34, 000= 3.4 x 10,000 = 3.4 x 104
d)
570,000 = 5.7 x 100,000 = 5.7 x 105
e) 1,200,000 = 1.2 x 1000,000 = 1.2 x 106
Using the quick method
Example 237000000
Place the decimal point between the 2 and 3 (2.37000000)
Then count the number of places that the decimal point has moved.
237000000 = 2.37 x 108
8 places
Slide 37
Converting Very Small Numbers into Standard Form
0.23 is not in standard form as the 1st digit is NOT between the 1 and 9
But 0.23 = 2 .3
10
So 0.23 =
2 .3
Remember to divide by 10 move the digits right
= 2.3 x 10–1
10
0.94 = 9.4 10 = 9.4 x 10–1
0.086 = 8.6 100 = 8.6 x 10–2
0.00034 = 3.4 10000 = 3.4 x 10–4
0.0057 = 5.7 1000 = 5.7 x 10–3
0.000012 = 1.2 100000 = 1.2 x 10–5
To convert standard form to ordinary numbers: Positive powers
1.31 x 105
Remember 105 means multiply by 10000
1.31 x 105 = 131000
To convert standard form to ordinary numbers: Negative powers
1.31 x 10–2
Remember 10–2 means
1.31 x 10–2 = 0.0131
1
10
2
1
So DIVIDE by 100
100
So if the power is positive, the ordinary number is BIG
If the power number is negative the ordinary number is small
Slide 38
Multiplying standard form
1.27 x 105 x 2.36 x 104
Separate the calculation into 2 parts as follows:
(1.27 x 2.36) x (105 x 104) = 2.9972 x 109
Rule of indices says we ADD the powers!
Division in Standard Form
4.8 x 107 ÷ 1.5 x 103
Separate into two parts
(4.8 ÷ 1.5) x (107 ÷ 103) = 3.2 x 10 (7-3) = 3.2 x 104
Rule of indices says subtract the powers!!
Sometimes we get a number that has a zero before the decimal point….0.742 x 1012
This can be rewritten as:
7.42 x 10-1 x 1012 = 7.42 x 1011
Rule of indices says ADD the powers
Standard Index form
Objective:
To convert numbers into
standard index form
Slide 2
Why is this number very difficult to use?
999,999,999,999,999,999,999,999,999
Too big to read
Too large to comprehend
Too large for calculator
To get around using numbers this large, we
use standard index form.
Slide 3
Reminder About Powers of 10
10 = 101
100 = 10 X 10 = 102
1000 = 10 X 10 X 10 = 103
10000 = 10 X 10 X 10 X 10 = 104
100000 = 10 X 10 X 10 X 10 X 10 = 105
Rule: Count the number of zeros
Slide 4
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
This means 2 in the hundreds so its worth 200
This means 3 in the tens so its worth 20
This means 5 in the units so its worth 5
This means 7 in the tenths so its worth
7
10
This means 1 in the hundreds so its worth
9
or 1.7
000
1
100
This means 9 in the thousandths so its worth
or .01
or .009
Slide 5
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
5
3
7
9
2
1
If you multiply by 10 all the digits move 1 place to the
left.
200 becomes 2000
30 becomes
300
5 becomes
50
So 235.719 X 10 =
2 3 5 .7 1 9
Slide 6
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
If you multiply by 100 all the digits move 2 places to the
left.
200 becomes 20000
30 becomes
3000
5 becomes
500
So 235.719 X 100 =
2 3 5.7 1 9
Slide 7
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
If you divide by 10 all the digits move 1 place to the
right.
200 becomes 20
30 becomes
3
5 becomes
5
.
So 235.719 10 =
2 3 5.7 1 9
Slide 8
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
If you divide by 100 all the digits move 2 places to the
right.
200 becomes 2
30 becomes 3
5 becomes 05
.
.
So 235.719 100 =
2 3 5 .7 1 9
Slide 9
Reminder about Place Value
Hundreds
Tens
Units
Tenths
Hundredths
Thousandt
hs
2
3
5
7
1
9
Instead of moving the digits most people think it easier
to move the point
.
235.719 x 10 = 2 3 5 7 1 9
.
235.719 x 100 = 2 3 5 7 1 9
.
235.719 100 = 2 3 5.7 1 9
235.719 10 = 2 3 5 7 1 9
But it is actually the
digits that move
Slide 10
Let’s investigate!
Converting large numbers
How could we turn the number 800,000,000,000 into
standard index form?
We can break numbers into parts to make it easier,
e.g. 80 = 8 x 10 and 800 = 8 x 100
800,000,000,000 = 8 x 100,000,000,000
And 100, 000,000,000 = 1011
So, 800,000,000,000 = 8 x 1011 in standard index form
Slide 11
Try it out!
How can we convert 30,000 into standard index
form?
Break into easier parts:
30000 = 3 x 10,000
And, 10,000 = 104
So 30,000 = 3 x 104 in standard index
form
The number is now easier to use
Slide 12
Now it’s your turn:
Copy down the following numbers, and convert them
into standard index form.
a) 500
= 5 x 100 = 5 x 102
b) 4000 = 4 x 1000 = 4 x 103
4
=
6
x
10,000
=
6
x
10
c) 60,000
d) 900,000 = 9 x 100,000 = 9 x 105
e) 7000,000 = 7 x 1000,000 = 7 x 106
Slide 13
One of the most important rules for writing
numbers in standard index form is:
The first number must be a value between
1 and 9
For example, 39 x 106 does have a value but it’s
not written in standard index form.
The first number, 39, is greater than 10.
But 39 = 3.9 x 10
So 39 x 106 = 3.9 x 10 x 106
Add powers
= 3.9 x 107
Slide 14
How could we convert 350,000,000 into
standard index form?
Again, we can break the number into smaller, more
manageable parts.
350,000,000 = 3.5 x 100,000,000
100,000,000 = 108
350,000,000 = 3.5 x 108 in standard index form
Slide 15
Try it out!
How can we convert 67,000 into
standard index form?
67,000 = 6.7 x 10,000
10,000 = 104
67,000 = 6.7 x 104 in standard index form
Slide 16
Now it’s your turn:
Copy out the following numbers and convert
them into standard index form.
a) 940
= 9.4 x 100 = 9.4 x 102
b) 8,600
= 8.6 x 1000 = 8.6 x 103
c) 34, 000
= 3.4 x 10,000 = 3.4 x 104
d) 570,000
= 5.7 x 100,000 = 5.7 x 105
e) 1,200,000
= 1.2 x 1000,000 = 1.2 x 106
Slide 17
Can you find a quick method of converting
numbers to standard form?
For example,
Converting 45,000,000,000 to standard form
Place a decimal point after the first digit
4.5000000000
10
Count the number of digits
after the decimal point.
This is our index number (our power of 10)
So, 45,000,000,000 = 4.5 x 1010
Slide 18
Using the quick method
Example 237000000
Place the decimal point between the 2
and 3 (2.37000000)
Then count the number of places that the
decimal point has moved.
237000000 = 2.37 x 108
8 places
Slide 19
Reminder about Negative
Powers
0.1=
1
10
10–1
1
0.01 =
100
1
0.001 =
0.0001=
1000
10–2
10–3
1
10000
10–4
Slide 20
Converting Very Small Numbers
into Standard Form
0.23 is not in standard form as the 1st digit is
NOT between the 1 and 9
But 0.23 =
2 .3
10
Remember to divide by 10
move the digits right
Using the rules of powers
So 0.23 =
2 .3
10
1
10
= 2.3 x 10–1
10–1
Slide 21
Converting Very Small Numbers
into Standard Form
0.056 is not in standard form as the 1st digit is
NOT between 1 and 9
But 0.056 =
5 .6
100
Remember to divide by 100
move the digits 2 places right
Using the rules of powers
So 0.056 =
5 .6
100
1
100
= 5.6 x 10–2
10–2
Slide 22
Converting Very Small Numbers
into Standard Form
0.00039 is not in standard form as the 1st digit is
NOT between 1 and 9
3 .9
Remember to divide by 10000
1 0 0 0 0 move the digits 4 places right
But 0.00039 =
Using the rules of powers
So 0.00039 =
3 .9
10000
1
10000
10–4
= 3.9 x 10–4
Slide 23
Now it’s your turn:
Copy out the following numbers and convert
them into standard index form.
a) 0.94
b) 0.086
= 9.4 10 = 9.4 x 10–1
= 8.6 100 = 8.6 x 10–2
c) 0.00034 = 3.4 10000 = 3.4 x 10–4
d) 0.0057
e) 0.000012
= 5.7 1000 = 5.7 x 10–3
= 1.2 100000 = 1.2 x 10–5
Slide 24
Converting to Normal Numbers
Slide 25
To convert standard form to ordinary
numbers: Positive powers
1.31 x 105
Write the digits 1 31
Hundreds
Tens
Remember 105 means
multiply by 10000
Units
Tenths
Hundredths
1
3
1
Thousandths
Now move all the digits 5 places left
But this is the same as moving the decimal point 5
places right
Slide 26
To convert standard form to ordinary
numbers: Positive powers
1.31 x 105
Write the digits 1 31
Hundreds
Tens
Units
Tenths
Hundredths
1
3
1
Which ever way you think about it the
number gets BIGGER
1.310000=
131000
1.310000= 1 3 1 0 0 0
Thousandths
Slide 27
To convert standard form to ordinary
numbers: Negative powers
1.31 x
10–2
Remember
Write the digits 1 31
Hundreds
Tens
10–2
means
1
10
2
1
100
So DIVIDE by 100
Units
Tenths
Hundredths
1
3
1
Thousandths
Now move all the digits 2 places right
But this is the same as moving the decimal point 2
places left
Slide 28
To convert standard form to ordinary
numbers: Negative powers
1.31 x
10–2
Remember
10–2
means
10
Write the digits 1 31
Hundreds
Tens
Units
Tenths
Hundredths
1
3
1
Which ever way you think about it the
number gets Smaller
01.31= 0 1 3 1
1.31= 0 1 3 1
1
2
1
100
Thousandths
Slide 29
The ordinary number is:
So if the power is positive, the
ordinary number is BIG
If the power number is negative the
ordinary number is small
Slide 30
Multiplying standard form
1.27 x 105 x 2.36 x 104
Separate the calculation into 2 parts as
follows:
(1.27 x 2.36) x (105 x 104)
= 2.9972
X
109
Rule of index
says we ADD the
powers!
Slide 31
Sometimes when we multiply out
the first part we can get more
than one digit before the decimal
point.
23.742 x 106
This can be rewritten as
Rule of
2.3742 x 10 x 106 indices
says we
which becomes
ADD
powers
2.3742 x 107
Slide 32
Division of Standard Form
If when we multiply standard form, we
add the powers, when we divide standard
form we-----
Subtract the powers
Slide 33
Division in Standard Form
4.8 x 107 ÷ 1.5 x 103
Separate into two parts
(4.8 ÷ 1.5)
x
3.2
x
(107 ÷ 103)
3.2 x 104
10(7-3)
Rule of
indices says
subtract the
powers!!
Slide 34
Sometimes we get a number that has a zero
before the decimal point….
0.742 x 1012
This can be rewritten as:
7.42 x 10-1 x 1012
7.42 x 1011
Rule of
indices
says ADD
the
powers
Slide 35
Standard Form
These are numbers of the type
a x 10n
Where a is a decimal number with only one digit in front (left) of the decimal point
n is a whole number that can be positive or negative
How can we convert 30,000 into standard index form?
Break into easier parts:
30000 = 3 x 10,000
And, 10,000 = 104
So 30,000 = 3 x 104 in standard index form
a)
500 = 5 x 100 = 5 x 102
b)
4000 = 4 x 1000 = 4 x 103
c)
60,000 = 6 x 10,000 = 6 x 104
d)
900,000 = 9 x 100,000 = 9 x 105
e)
7000,000 = 7 x 1000,000 = 7 x 106
Slide 36
One of the most important rules for writing numbers in standard index form is
The first number must be a value between 1 and 9
For example, 39 x 106 does have a value but it’s not written in standard index form.
The first number, 39, is greater than 10.
But 39 = 3.9 x 10
So 39 x 106 = 3.9 x 10 x 106 = 3.9 x 107
a)
940 = 9.4 x 100 = 9.4 x 102
b)
8,600= 8.6 x 1000 = 8.6 x 103
c)
34, 000= 3.4 x 10,000 = 3.4 x 104
d)
570,000 = 5.7 x 100,000 = 5.7 x 105
e) 1,200,000 = 1.2 x 1000,000 = 1.2 x 106
Using the quick method
Example 237000000
Place the decimal point between the 2 and 3 (2.37000000)
Then count the number of places that the decimal point has moved.
237000000 = 2.37 x 108
8 places
Slide 37
Converting Very Small Numbers into Standard Form
0.23 is not in standard form as the 1st digit is NOT between the 1 and 9
But 0.23 = 2 .3
10
So 0.23 =
2 .3
Remember to divide by 10 move the digits right
= 2.3 x 10–1
10
0.94 = 9.4 10 = 9.4 x 10–1
0.086 = 8.6 100 = 8.6 x 10–2
0.00034 = 3.4 10000 = 3.4 x 10–4
0.0057 = 5.7 1000 = 5.7 x 10–3
0.000012 = 1.2 100000 = 1.2 x 10–5
To convert standard form to ordinary numbers: Positive powers
1.31 x 105
Remember 105 means multiply by 10000
1.31 x 105 = 131000
To convert standard form to ordinary numbers: Negative powers
1.31 x 10–2
Remember 10–2 means
1.31 x 10–2 = 0.0131
1
10
2
1
So DIVIDE by 100
100
So if the power is positive, the ordinary number is BIG
If the power number is negative the ordinary number is small
Slide 38
Multiplying standard form
1.27 x 105 x 2.36 x 104
Separate the calculation into 2 parts as follows:
(1.27 x 2.36) x (105 x 104) = 2.9972 x 109
Rule of indices says we ADD the powers!
Division in Standard Form
4.8 x 107 ÷ 1.5 x 103
Separate into two parts
(4.8 ÷ 1.5) x (107 ÷ 103) = 3.2 x 10 (7-3) = 3.2 x 104
Rule of indices says subtract the powers!!
Sometimes we get a number that has a zero before the decimal point….0.742 x 1012
This can be rewritten as:
7.42 x 10-1 x 1012 = 7.42 x 1011
Rule of indices says ADD the powers