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

Then

10³ 10² =10^3-2

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 :-

	We are saying, in a thousand unit, how many 1/100ths are there ?
We have moved the divisor to above the line and changed the sign. This is a basic Rule or Indices manipulation and can be very useful
So you will find that :-
We are still following the same rule of "Multiply the top and bottom by the same number", which does not change the actual value.
So from above and

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

Let's move on