Download 220 SIF 1 - Brain

Standard Index Form 1
Objectives: Change between
ordinary and SIF numbers
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What is Standard Index Form?
In technical, medical and scientific work,
sometimes it is necessary to deal with numbers
that have lots of noughts.
A number with lots of noughts is clumsy and
it’s easy to make a mistake with the noughts so
we can use a method called standard index
form like this:
3 000 000 = 3 x 106
Three million
written in the
normal way
Three million
written in
standard index
form
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How to write a number in S.I.F.
To write, for example, 300 000 in
SIF, we would use powers of 10
like this…
300000 = 3 x 100000
= 3 x 105
This number
must be bigger
than 1 and
smaller than
10
102 =
103 =
104 =
105 =
106 =
100
1000
10000
100000
1000000
etc
The power of 10
that gives an
equal value
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How to write a number in S.I.F.
Here is another example of how
to write 1 250 000 in SIF
1 250 000 = 1.25 x 100000
= 1.25 x 106
This number
must be bigger
than 1 and
smaller than
10
102 =
103 =
104 =
105 =
106 =
100
1000
10000
100000
1000000
etc
The power of 10
that gives an
equal value
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Write these numbers in standard index form
1.
3000000  3 x 1000000  3 x 106
2.
240000  2.4 x 100000  2.4 x 105
3.
3400  3.4 x 1000  3.4 x 103
4.
12500  1.25 x 10000  1.25 x 104
5.
3750000  3.75 x 1000000  3.75 x 106
6.
120000  1.2 x 100000  1.2 x 105
7.
17500000  1.75 x 10000000  1.75 x 107
8.
4560000  4.56 x 1000000  4.56 x 106
9.
10.
75000000  7.5 x 10000000  7.5 x 107
125000  1.25 x 100000  1.25 x 105
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Change SIF numbers into
ordinary numbers
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To change 8.75 x 107
into an ordinary
number, we would…
8.75 x 105  8.75 x 100000  875000
Write out
what the
number
means
Do the
multiplication
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Write these SIF numbers as ordinary numbers
1.
4 x 103  4 x 1000  4000
2.
2 x 104  2 x 100000  20000
3.
4.
1.5 x 103  1.5 x 1000  1500
3.75 x 104  3.75 x 10000  37500
5.
2.5 x 106  2.5 x 1000000  2500000
6.
4.7 x 102  4.7 x 100  470
7.
8.
9.
10.
1.25 x 105  1.25 x 100000  125000
3.1 x 107  3.1 x 10000000  31000000
6.25 x 104  6.25 x 10000  62500
7.5 x 106  7.5 x 1000000  7500000
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Use SIF to represent small numbers
Small numbers also contain lots of
noughts. It is easy to add or miss out a
nought in a number like 0.000012 so SIF
can be use to represent these like this…
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To write 0.000012
in SIF, we would
Decimal point
needs to move 5
times  -5
0.000012 = 1.2 x 10-5
102 = 100
101 = 10
100 = 1
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
10-4 = 0.0001
10-5 = 0.00001
etc
Write the as a number
bigger than 1 and
smaller than 10
Use the appropriate
power of 10 to make
the two numbers equal
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Write these numbers in standard index form
1.
0.000007 = 7 x 10-6
2.
0.000000005 = 5 x 10-9
3.
0.000125 = 1.25 x 10-4
4.
0.000075 = 7.5 x 10-5
5.
0.000625 = 6.25 x 10-4
6.
0.000067 = 6.7 x 10-5
7.
0.00043 = 4.3 x 10-4
8.
0.056 = 5.6 x 10-2
9.
10.
0.000000875 = 8.75 x 10-7
0.0000045 = 4.5 x 10-6
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Write these SIF numbers as ordinary numbers
1.
8 x 10-5 = 0.00008
2.
7 x 10-6 = 0.000007
3.
9 x 10-5 = 0.00009
4.
3.5 x 10-7 = 0.00000035
5.
2.5 x 10-8 = 0.000000025
6.
4.7 x 10-9 = 0.0000000047
7.
1.25 x 10-8 = 0.0000000125
8.
1.375 x 10-7 = 0.0000001375
9.
10.
8.75 x 10-6 = 0.00000875
1.125 x 10-10 = 0.000000000125
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