Bredhurst Receiving and Transmitting Society
Advanced Radio Amateur Examination
maths...So what is next
So what is next ??
There are two more mathematical function as well as addition - subtraction - multiplication and division Powers of numbers and Roots of numbers.
Powers of numbers greater and less than one
Number greater than one
If two numbers are multiplied together it means the same as the number being raised the value by the power of 2.
3 x 3 = 9 but we could have had 32= 9 then little 2 up a little bit means multiply the number by itself which is also called squared.
What is we have 3 x 3 x 3 = 27
Which could have written that as 33= 27 which is also called cubed
and we can go on 3 x 3 x 3 x 3 = 81 which could have written that as 34= 81
The little number raised above the line is also called the index number and is an especially good way of expressing very large numbers.
What is 1.0 x 10 x 10 x 10 x 10 x 10 x 10 ?
1.0 x 10 x 10 = 100 = 1.0 x 102
1.0 x 10 x 10 x 10 = 1000 = 1.0 x 103
1.0 x 10 x 10 x 10 x 10 = 10000 =1.0 x 104
1.0 x 10 x 10 x 10 x 10 x 10 = 100000 =1.0 x 105
1.0 x 10 x 10 x 10 x 10 x 10 x 10 = 1000000 = 1.0 x 106
Check the original sum and you will see that we had 6 zeros and we have 6 zeros after the 1 in the answer there is a little 6 beside the 10 which you can now understand means move the decimal point 6 places to the right.
In the examples above we showed the figure of 1.0 x to indicate what we were raising to what power. From now on we must understand that the 1.0 x is still there but will now be omitted.
This leads us to multiplying and dividing powers of 10
102 x 103 = 10 x 10 times 10 x 10 x 10 = 100 times 1000 = 100000
but we could have looked at like this
102 x 103 =102+3 = 105 = 1 with 5 zeros = 10000
101 = 1 with 1 zeros =
the divide by 102 becomes 10-2
try it on your calculator
1000 / 100 and see what you get ???
Numbers less than one
Now above we mentioned 10-2
The use of the -2 means divide one by 10 x 10 which gives 0.01
But let's start at the beginning
10-1 = 110 = 0.1
10-2 = 1 10 x 10 = 0.01
10-3 = 1 10 x 10 x 10 = 0.001
This last one is important as it represents 1 1000 which is the milli.
so 10mA could be written as 10 x 10-3 and in fact this is used in the section on tuned circuits
What happens if we want to divide indices :-
|If you want to see more on the use of powers then
click here and go to the section
Roots of numbers
An so we move onto the last part of the maths needed for the exam - well understanding the basics of the maths (you will understand more as you get into the site !!).
We have seen that 3 x 3 = 9
So if you were asked what number multiplied by itself gives you 9 you would I hope you would say 3 -
You have just taken what is called the square root of 9 - so you are not so dim after all.
So if you were asked what number multiplied by itself gives you 144 you might have to think a bit and might come up with 12 - 12 x 12 = 144
BUT if you were asked what number multiplied by itself gives you 9801 you would probably look into you tea or coffee cup and think it was time to make a drink and deal with that later.
Well help is at hand in the form of a calculator which has the square root sign on it.
So we could write "What is the ?? "
and you would still understand that the wanted answer is a number which when multiplied by itself gives you 9801 --- ok ??
In fact the answer is 99 try on your simple calculator 99 x 99 and it gives you ???
If you have a calculator with the enter the number 9801 and press the key and the answer 99 will appear !!! I hope !!!
Sometimes the calculator will need you to enter 9801 first and then press the Square Root button. You need to get to know your calculator.
In fact the symbol is not normally written as large and you would normally see it as - the bar line over the top of the number indicate that you want the square root of the number below the line.
So is the everything ?
Eh! well no we have still to consider 1/n which means 1 divided by any number and pi