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- baby456

please help i dont understand the metric system!
1.how many cm woud be in a kilometer
and i have another question
2.The daily recommendation for vitamimn a 800 micro grams how many grams is this

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- welshfella

1 meter = 100 centimeters
1 meter = 1000 millimeters
1 kilometer = 1000 meters

- welshfella

so there are 100 * 1000 cms in a kilometer

- welshfella

1 microgram = 1 millionth of a gram
so
1 gram = 1,000,000 micrograms

- welshfella

800 micro grams = 800 / 1.000,000 grams

- baby456

@welshfella help me

- welshfella

well you need to divide 800 by 1,000,000
try it on your calculator

- whpalmer4

\[100 \text{ cm} = 1 \text{ m}\]divide both sides by 1m to give
\[\frac{100\text{ cm}}{1\text{ m}} = \cancel{\frac{1\text{ m}}{1\text{ m}}}=1\]
Now, we know we can multiply anything by 1 and still get the same value, so we can multiply any quantity of meters by that fraction we just made to convert it to cm.
Similarly, \[1000\text{ m} = 1\text{ km}\]We want to convert from km to meters so we need km in the denominator. Divide both sides by 1 km:
\[\frac{1000\text{ m}}{1 \text{ km}} = \cancel{\frac{1\text{ km}}{1\text{ km}}} =1\]so that gives us our conversion factor from km to meters.
To work our problem:
\[1\text{ km}*\frac{1000\text{ m}}{1\text{ km}}*\frac{100\text{ cm}}{1\text{ m}} = 1\cancel{\text{ km}}*\frac{1000\text{ m}}{1\cancel{\text{ km}}}*\frac{100\text{ cm}}{1\text{ m}}\] \[=1*\frac{1000\cancel{\text{ m}}}{1}*\frac{100\text{ cm}}{1\cancel{\text{ m}}} = 1*1000 * 100 \text{ cm} = 100000 \text{ cm}\]
By doing the work in this manner, and carefully canceling the units as I did, you get built-in error checking. Doing it by simply multiplying or dividing gives you no such error checking, and it is easy to multiply when you should have divided, or divide when you should have multiplied.

- anonymous

@whpalmer4 Has given an excellent answer. If you watch your units in your calculations you gain incredible insight into your problems in chemistry, physics, and advanced mathematics. It's one of the few great skills to learn that if you understand it, your problems will seem to solve themselves sometimes, since there is usually only one way of arranging your values so that the units match up in a sensible way.
If you want to know a distance, your answer better end up in some units of distance not in some units of time or squared distance or something funky.

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