Once upon a time a shopkeeper sold a great many small items to lots of customers. Here I have chosen to tell the story ~ and show pictures ~ of just one of the many items sold ~ steel washers.
If any shopkeeper spends too much time counting items for every customer ~ one ~ two ~ three ~ four ~ on ~ and on ~ then a queue will form.
Customers get grumpy if they have to wait in a queue. The shopkeeper decided to pack the washers into envelopes. Each envelope contains ten washers. Pictorially it looks like this ~
Because of lots of things ~ the speedy service being one of them ~ the shopkeeper's trade flourished. People were buying a great many items at every visit.
If someone wanted forty-three washers the shopkeeper would hand over four envelopes and also three single washers ~ that was much quicker than counting up to forty-three.
Everyone thought using envelopes was a good idea. Trade increased. The shopkeeper bundled ten envelopes into a package and tied it with string. Ten envelopes ~ each with ten washers ~ that means one hundred washers.
Here are three quick questions to check how things are going for you ~
After some time the shopkeeper had to send someone to go to the stationery shop to buy more envelopes ~ stocks kept running low.
Someone on the staff pointed out that the number of envelopes being used could be saved. The suggestion was made to put the washers straight into boxes ~ one hundred to a box. In that way there would also be a handy storage facility for the end-user.
Here is a short summary of the maths that was going on.
To return to our story ~ the shopkeeper had obviously had a good mathematical education. He chose to work in tens ~ ten washers ~ ten envelopes ~ maybe next year it will be ten boxes fit into one carton.
As a further update to the story ~ the shopkeeper is now a manufacturer of washers ~ with a huge factory ~ and living happily ever after.
Back to thinking about maths ~ hmmm ~ with ten boxes to one carton ~ how many washers in one carton?
Does a van take ten cartons?
Will ten vanloads fit into one container?
How many containers fit onto a train?
How many trainloads fit into a ship?
Finally ~ how many washers in a shipload?
The answer is ~ quite a lot!
Working in tens is what mathematicians do. Sometimes they are not very imaginative. Instead of parcelling things into envelopes ~ bundles ~ cartons ~ whatever ~ they use a different system.
They use labels ~ ones ~ tens ~ hundreds ~ thousands ~ tens-of-thousands ~ and so on. Some people call the 'ones' units. It means the same as ones or singles.
In shorthand ~ or in maths-code if you wish ~ we could have ~
thousands ~ hundreds ~ tens ~ units
T ~ H ~ T ~ U
thousands ~ hundreds ~ tens ~ ones
T ~ H ~ T ~ O
The important thing to note is that any one item is ten times greater than the one beside it on the right.
Not everyone works in tens when packaging ~ sometimes it is convenient to work in some other quantity .
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