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You may
think that you know everything about counting...
but I may have a few surprises for you. We use what is called a "base
ten"
counting system. This is because we have numbers from 0 to 9, then we
start
a new column and use the numbers over again. Actually... one of the
greatest
advancements in numbers was the invention of ZERO.
Before zero was invented it was difficult to
describe no objects. If
you had two sheep, you could record this with two lines drawn into
clay,
carved in wood, or whatever. But if you sold both of your sheep... what
would you do? You could have a clay or wood tablet with nothing written
on it... but then how would you know if that was an accurate count for
the day... or if your accountant just forgot to write it down?
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Originally simple marks were made. To keep the
information from being
too confusing people began to group the data by making a diagonal line
to show every five objects. This was the beginning of written numbers.
Different cultures started to develop their own system of numbers.
Standardization
was needed for trade between many cultures. |
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The Romans started to use a set of numbers that
was accepted as a standard
for quite a long time. They started off using I
for one, II
for two and III
for three. We will get to four in just a second. The Romans got the
idea
to use a V
for the number five from
the hand. see the image to the left. They decided to show subtraction
by
putting numbers on the left... so the number four became IV.
The Romans were not too fussy... so sometimes it was also written IIII. |
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You might think that the Romans would put two
hands together to get W
or VV
for ten... but they used X
instead. Many believe that they derived it like the image to the left,
but we will never know for sure. This means that the Roman numbers
looked
something like this:
| I |
II |
III |
IV |
V |
VI |
VII |
VIII |
IX |
X |
| XI |
XII |
XIII |
XIV |
XV |
XVI |
XVII |
XVIII |
XIX |
XX |
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The Romans decided that 100 was an important
number, so they started
to use C
for 100. After awhile, they
cut C
in half and came up with L
for 50. This means that the number 150 would be written CL. |
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The Romans used M for 1,000 then came up with D
for 500. Some say the
D came from an M cut in half... if you use the image to the left you
can
sort of understand where this idea came from. |
The Arabs started to use
ten symbols for the numbers 0
through 10. They understood the concept of using a symbol to represent
the lack of something. It was also useful as a placeholder to show
values
beyond 10. From these symbols our modern numbers were developed.
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If you notice, our hands each usually have five
digits. We have a nice
set of two, so we can count to ten with ease. Our numbers are therefore
based on ten digits. When we go above ten, we add another column to
show
that the number is larger than what we can count with our hands. It
could
be said that we use a BASE
TEN numbering
system because we have based our method of counting on ten.
What would have happened if we had six fingers
on each hand? Can you
see that we likely would have developed a BASE TWELVE counting system?
You should be able to see that things would have been a bit different.
In the next section we will be looking at some other numbering systems.
Computers store numbers using a different numbering system... but don't
panic... we will go slowly and learn about this.
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