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Dollars and the Metric Prefixes


Date: 01/11/2002 at 21:28:19
From: Desiree
Subject: How do you do problems like 1.2km = _dam?

I can't do problems that involve km, dm, mm, dam, m, etc.
Can you help me?


Date: 01/12/2002 at 00:32:04
From: Doctor Ian
Subject: Re: How do you do problems like 1.2km = _dm?

Hi Desiree,

Can you convert dollars to pennies? If so, then you can convert meters 
to centimeters and millimeters.  

The prefix 'centi-' means '1/100th', so a centimeter is 1/100 of a 
meter, and a centidollar is 1/100 of a dollar, which is the same as a 
penny.  

A decimeter would be 1/10 of a meter, and a decidollar would be a 
dime.

You can convert back and forth between pennies and dimes and dollars 
and ten dollar bills and so forth, just by multiplying and dividing by 
10. (Of all the things you could multiply or divide by, 10 is the 
easiest one, because all you have to do, really, is add zeros and move 
the decimal point around.) 

It works the same way for the various distances. 

Here would be the money equivalents if we used metric prefixes for 
dollars:

   1 kilodollar  = $1000 dollars
   1 hectodollar = $100 
   1 decadollar  = $10
   1 dollar      = $1
   1 decidollar  = 10 cents

   1 centidollar = 1 cent
   1 millidollar = 1/10 of a cent

Here are the distance equivalents:

   1 kilometer  = 1000 meters
   1 hectometer = 100 meters
   1 decameter  = 10 meters
   1 meter      = 1 meter
   1 decimeter  = 1/10 of a meter

   1 centimeter = 1/100 of a meter
   1 millimeter = 1/1000 of a meter

Rather than remembering a bunch of conversions between the different 
prefixes, it's probably easier to just convert to the standard, and 
then to whatever you want to get to.  For example, 

                                 100 centidollars
   1 hectodollar = 100 dollars * ---------------- 
                                   1 dollar

                 = 100 * 100 centidollars

                 = 10,000 centidollars (pennies)

So how do you remember all these prefixes? Some of them you can figure 
out from words that you already know. For example, 'decimal' comes 
from the prefix 'dec', which means 10. So 'deci' and 'deca' would both 
have to do with 10, and you just have to remember which is which. (I 
keep them straight by remembering that the prefixes that end in 'i' 
tend to make things smaller rather than larger: 'deci-', 'centi-', 
'milli-'.)

Similarly, words like 'century' (100 years) and 'centipede' (100 legs) 
come from the prefix 'cent', which means 100. The word 'percent' also 
comes from this root, and 'percent' literally means 'for each 100'.  

The other ones, you just have to memorize. Sorry! In a perfect world, 
'kilo' would be 'milla', and 'hecto' would be 'centa', so it would 
look like

   1 millameter = 1000 meters
   1 centameter = 100 meters
   1 decameter  = 10 meters
   1 meter      = 1 meter
   1 decimeter  = 1/10 of a meter

   1 centimeter = 1/100 of a meter
   1 millimeter = 1/1000 of a meter

which would reduce the amount that you'd have to remember, but it 
would be tough to tell sometimes whether someone was saying 
'centimeter' or 'centameter', or 'millimeter' or 'millameter', so 
maybe it's not such a good idea after all. (Note that there is no 
confusion between 'deci', in which the 'c' sounds like an 's', and 
'deca', in which the 'c' sounds like a 'k'.)

I suppose it's not that much different from having to remember that 
some verbs have irregular forms, like 'slept' instead of 'sleeped' and 
'bought' instead of 'buyed'.  

Does this help? Write back if you have more questions, about this or 
anything else. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Middle School Terms/Units of Measurement

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