Monday Maths: Number Systems

Did you know that our current decimal numbering system was inherited from the Arabs?  They were the ones who invented the positional numbering system – using only ten symbols and positioning them differently to represent units, tens, hundreds and so on.

But there are many other types of numbering systems, and some of them are quite fun.

Roman Numerals

Important if you want to know when TV shows were first made, because the copyright notice at the very end of the credits is written in them.  Does anyone know why that is, by the way?  I’d love to know.

Roman Numerals work like this:

I – one 
V – five 
X – ten 
L – fifty 
C – one hundred 
D – five hundred 
M – one thousand

If you want numbers in between the available symbols, you have to use combinations.  Putting the smaller number before the larger means take it away, and the smaller after the larger is add.

I = 1 
II = 1 + 1 = 2 
III = 1 + 1 + 1 = 3 
IV = 5 – 1 = 4 
V = 5 
VI = 5 + 1 = 6 
… 
IX = 10 – 1 = 9 
X = 10 

So, many of my favourite shows growing up had (c) MCMXCIII or similar at the end of the credits.  That dates me, doesn’t it!

Why not challenge the girls to write down their age, birthdate, or shoe size in roman numerals?

Binary

If you’ve got any girls who want to get into computers, this is a good one.  Our decimal number system is in base 10 – you have ten symbols, count from 0 to 9 and then start on the next column over.

For example:

Base 10     Binary is in base 2 – so it only uses 0s and 1s.  Like this:

Base 2

Writing big numbers in binary is a pain (many of my Brownies were born in the year 11111010101), so stick to children’s ages or the current day of the month, rather than year of birth or anything like that!

For example, Brownies are aged 111, 1000, 1001, 1010, and sometimes even 1011.

Hieroglyphic Numbers

If that last section confused you, you’ll be glad to know that the Egyptians worked in base 10, just like us.  However, instead of using the positioning of the numbers to represent how big they were, they used different symbols.

All you have to do is write the right number of the right kind of symbol.  The exact positioning isn’t important, although you should go in order from largest to smallest.  You just have to make them look pretty and neat.

Why not have a go at creating your very own hieroglyphs?

See here for pretty pictures: click me.

Braille

Braille is named after its creator, Frenchman Louis Braille, who went blind following a childhood accident. In 1824, at the age of 15, Braille developed his code for the French alphabet, and it has since been developed and improved on.

The system consists of raised dots arranged in patterns which can be read with the finger.  It takes a bit of practice to be able to distinguish between them without looking!

There are three levels of Braille in English.  Grade 1 is a straight transliteration of the alphabet and numbers, and is used to teach basic literacy.  Grade 2 includes words, abbreviations and so on, and is the version in common use.  Grade 3 is personal shorthand, which varies between people.

We’re only worried about Grade 1 here.  It’s in common use on everyday items – did you know that it’s a legal requirement for medicines to carry their name in braille?  One good thing that’s come out of the EU.

Click on the image to go to a website with more detail.

You can make braille using fancy machines (my tutor at uni was blind, and he had some pretty funky machines in his office), but you can also do it with things you probably have in your cupboard.  Try placing a piece of paper on a soft surface and using a blunt pencil to make impressions.  Remember that the dots have to be raised, so you need to punch from the back of the paper.

Use braille to send secret messages to each other!

What other number systems can you think of?

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