IES Rafael ReyesMaths 1º ESO
Standard Index Form
José Antonio Sayago
Objective:
To convert numbers into standard index form
Standard Index form
999,999,999,999
Why is this number very difficult to use?
Too big to readToo large to comprehendToo large for calculator
To get around using numbers this large, we use standard index form.
We can round it up to: 1,000,000,000,000
So at the very least we can describe it as 1 with 12 noughts.
But it still not any easier to handle!?!
How could we turn the number 800,000,000,000 into standard index form?
Let’s investigate!Converting large numbers
800,000,000,000 = 8 · 100,000,000,000
We can break numbers into parts to make it easier,e.g. 80 = 8 · 10 and 800 = 8 · 100
And 100, 000,000,000 = 1011
So, 800,000,000,000 = 8 · 1011 in standard index form
Try it out!How can we convert 30,000 into standard index form?
Break into easier parts:30000 = 3 · 10,000 And, 10,000 = 104
So 30,000 = 3 · 104 in standard index form
The number is now easier to use
= 9 · 100,000 = 9 · 105
Now it’s your turn:
Copy down the following numbers, and convert them into standard index form.
a)500b)4000c) 60,000d)900,000e)7000,000
= 5 · 100 = 5 · 102
= 4 · 1000 = 4 · 103
= 6 · 10,000 = 6 · 104
= 7 · 1000,000 = 7 · 106
One of the most important rules for writing numbers in standard index form is: The first number must be a value between
1 and 10
For example, 39 · 106 does have a value but it’s not written in standard index form.The first number, 39, is greater than 10.
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 · 100,000,000100,000,000 = 108
350,000,000 = 3.5 · 108 in standard index form
Try it out!How can we convert 67,000 into standard index form?
67,000 = 6.7 · 10,000
10,000 = 104
67,000 = 6.7 · 104 in standard index form
Now it’s your turn:
Copy out the following numbers and convert them into standard index form.
a) 940b) 8,600c) 34, 000d) 570,000e) 1,200,000
= 9.4 · 100 = 9.4 · 102
= 8.6 · 1000 = 8.6 · 103
= 3.4 · 10,000 = 3.4 · 104= 5.7 · 100,000 = 5.7 · 105
= 1.2 · 1000,000 = 1.2 · 106
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 Count the number of digits after the decimal point.
10This is our index number (our power of 10)
So, 45,000,000,000 = 4.5 · 1010