ARITHMETIC BASES
 
 
Different cultures and civilizations around the world have used a variety of methods for counting and calculating stuff.
 

Before many western countries adopted the metric system (everything based on 10) many bases were used on a daily basis!!

Think of yards, feet and inches :12 inches = 1 foot, 3 feet = 1 yard, 22 yards = 1 chain, 10 chains = 1 furlong and 8 furlongs = 1 mile (non't forget the rods, the pole, and the perch!)

Look at the root bases here: base 12, base 3, base 22, base 8 (octals).

Then there were pounds, shillings and pennies (not to mention guineas): bases 12, and 20 (and 21)

And then there's weight: Hum: ounces, pounds, stones, quarters, hundredweights and tons: 16 oz = 1lb, 14 lb = 1 stn, 2 stn = 1 qtr, 4 qtrs = 1 cwt and
20 cwt = 1 ton (2240 lb);
What are the bases?

Time: we don't tell time in 10s, what base(s) do we use?

What other bases can you think of?

 

 

 

To help comprehend bases, use the circle at the side.

It's set up like a clock with a 5 hour day, go round 3 times and 3 days are passed.

You can use the clock idea with/for any base. For example base 6.

What digits would be on the "6" face?

Where do you see both base 12 and base 60 in the same place?

Try adding each of these:

Now try subtracting them!

 
  Are you not happy that we use mostly base 10 now? BUT. . . . .