Standard Index form

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Standard Index form

• OCR Module 8

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Why is this number very difficult to use?
999,999,999,999,999,999,999,999,999,999
Too big to read
Too large to comprehend
Too large for calculator
To get around using numbers this large, we use
standard index form.
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Look at this 100,000,000,000,000,000,000,000,000,0
00
At the very least we can describe it as 1 with 29
noughts.
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Lets investigate!
Converting large numbers
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
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Try it out!
How can we convert 30,000 into standard index
form?
Break into easier parts
The number is now easier to use
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Now its your turn
Copy down the following numbers, and convert them
into standard index form.

• 500
• 4000
• 60,000
• 900,000
• 7000,000

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One of the most important rules for writing
numbers in standard index form is
But NOT 10 itself!!
For example, 39 x 106 does have a value but its
not written in standard index form. The first
number, 39, is greater than 10.
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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
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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
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Now its your turn
Copy out the following numbers and convert them
into standard index form.

• 940
• 8,600
• 34, 000
• 570,000
• 1,200,000

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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
Count the number of digits after the decimal
point.
This is our index number (our power of 10)
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And numbers less than 1?
How can we convert 0.067 into standard index form?
0.067 6.7 x 0.01
0.01 10-2
0.067 6.7 x 10-2
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And numbers less than 1?
How can we convert 0.000213 into standard index
form?
0.000213 2.13 x 0.0001
0.0001 10-4
0.000213 2.13 x 10-4
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And numbers less than 1?
How can we convert 0.00603 into standard index
form?
0.00603 6.03 x 0.001
0.0001 10-3
0.00603 6.03 x 10-3
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Now its your turn
Copy out the following numbers and convert them
into standard index form.

• 0.094
• 0.00039
• 0.903
• 0.000452
• 0.00624

9.4 x 0.01
9.4 x 10-2
3.9 x 10-4
3.9 x 0.0001
9.03 x 0.1
9.03 x 10-1
4.52 x 10-4
4.52 x 0.0001
6.24 x 0.001
6.24 x 10-3
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Calculations
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Multiply two numbers
4 x 1018 x 3 x 104
Numbers
Powers of 10
4 x 3
x 1018 x 104
ADD powers
12
x 1022
NOT Std Form!
1.2 x 101
x 1022
1.2 x 1023