1. Standard Index form
OCR Module 8

2. 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.

3. But it still not any easier to handle!?!
Look at this
100,000,000,000,000,000,000,000,000,000
At the very least we can describe it as 1 with 29 noughts.
But it still not any easier to handle!?!

4. 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
Size given by first number 8 and the index 11
And 100, 000,000,000 = 1011
So, 800,000,000,000 = 8 x 1011 in standard index form

5. So 30,000 = 3 x 104 in standard index form
Try it out!
How can we convert 30,000 into standard index form?
Break into easier parts:
And, 10,000 = 104
30000 = 3 x 10,000
So 30,000 = 3 x 104 in standard index form
The number is now easier to use

6. Now it’s your turn: 500 = 5 x 100 = 5 x 102 4000 60,000
Copy down the following numbers, and convert them into standard index form.
500
4000
60,000
900,000
7000,000
= 5 x 100 = 5 x 102
= 4 x = 4 x 103
= 6 x 10,000 = 6 x 104
= 9 x 100,000 = 9 x 105
= 7 x 1000,000 = 7 x 106

7. The first number must be a value between
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
But NOT 10 itself!!
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.
Pupils should copy down rule in green

8. 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
3.5 x 100 = 350, x by 1,000,000 makes 350,000,000
350,000,000 = 3.5 x 108 in standard index form

9. Try it out! How can we convert 67,000 into standard index form?
10,000 = 104
67,000 = 6.7 x 104 in standard index form

10. Now it’s your turn:
Copy out the following numbers and convert them into standard index form.
940
8,600
34, 000
570,000
1,200,000
= 9.4 x 100 = 9.4 x 102
= 8.6 x 1000 = 8.6 x 103
= 3.4 x 10,000 = 3.4 x 104
= 5.7 x 100,000 = 5.7 x 105
= 1.2 x 1000,000 = 1.2 x 106

11. 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
Count the number of digits after the decimal point.
Pupil book G3 page 137 10
This is our index number (our power of 10)
So, 45,000,000,000 = 4.5 x 1010

12. And numbers less than 1?
How can we convert into standard index form?
0.067 = 6.7 x 0.01
0.01 = 10-2
0.067 = 6.7 x 10-2

13. And numbers less than 1?
How can we convert into standard index form?
= 2.13 x
= 10-4
= 2.13 x 10-4

14. And numbers less than 1?
How can we convert into standard index form?
= 6.03 x 0.001
= 10-3
= 6.03 x 10-3

15. Now it’s your turn:
Copy out the following numbers and convert them into standard index form.
0.094
0.903
= 9.4 x 0.01
= 9.4 x 10-2
= 3.9 x
= 3.9 x 10-4
= 9.03 x 0.1
= x 10-1
= 4.52 x
= x 10-4
= 6.24 x 0.001
= x 10-3

16. Calculations

17. Multiply two numbers 4 x 1018 x 3 x 104 4 x 3 x 1018 x 104 = 12 x 1022
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