how do you do conversions

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- anonymous

how do you do conversions

- katieb

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- anonymous

Which type of conversions?

- anonymous

Well these are like 1.42g/cm to mg/mm

- anonymous

and stuff like any conversions i dont get

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## More answers

- anonymous

Well, lets say..... How many mg are there in x g?
It should be there are 1,000 milligrams (mg) in 1 gram (g). To get your answer, simply multiply x by 1000.
Do you get this one?

- anonymous

1gm=1000 mg
1cm=10 mm

- anonymous

well i think so but its still difficult and im only in ninth grade

- mathstudent55

Every conversion factor can be written as a fraction that equals 1.
Then you use the conversion factor by multiplying in a way that cancels the unit you don't want and leaves the unit you want.

- anonymous

@mathstudent55 i go that part so that helps which i understand but i dont get the ones with a bunch of measurements

- anonymous

like 8.24 g/cm to mg/mm

- mathstudent55

Here is an example.
Convert 234 kg to g
\(1~kg = 1000~g\)
We divide both sides by 1kg to get:
\( 1 = \dfrac {1000~g}{1~kg} \)
If we divided both sides by 1000 g, then we'd get:
\(\dfrac{1~kg}{1000~g} = 1\)
Since both of these conversion fractions are equal to 1, they are also equal to each other.
\(\dfrac{1~kg}{1000~g} = \dfrac{1000~g}{1~kg} = 1\)
Because of the multiplicative identity, 1, multiplying a number by 1 does not change the number, so we can multiply a mass in kg or in g by one of these conversion factors without changing the amount, and only changing the form.

- anonymous

uhhhhhhhhhhhh

- mathstudent55

This shows you that every conversion factor can be written as a fraction. You can have it always two ways, one being the reciprocal of the other. Then you use the one you need.

- mathstudent55

Going back to my example above.
Convert 234 kg to grams.
\(\large 234 \cancel{kg} \times \dfrac{1000~g}{1~\cancel{kg}} = 234,000 ~g\)
The conversion fractions from kg to g and g to kg are
\(\dfrac{1~kg}{1000~g}\) and \(\dfrac{1000~g}{1~kg}\)
How do you know which one to choose?
You choose the one that will cancel the units you don't want ad will leave the units you want.
Since in this example we wanted to convert from kg to g, we want g and do not want kg.
234 kg times (1000 g)/(1 kg) cancels out kg leaving g.

- mathstudent55

Now we can do your example.

- mathstudent55

You need to convert \(\large 1.42 \dfrac{g}{cm} \) to \(\large \dfrac{mg}{mm} \)
The first step is to make sure you know the conversion factors:
1 g = 1000 mg
1 cm = 10 mm
Ok so far?

- mathstudent55

The conversion factors will be written as fractions and will be multiplied. We just need to figure out which way to write the conversion fractions, since each conversion fraction can be written 2 ways.
Let's convert from g to mg first.
g is in the numerator, so we need g in the denominator to cancel out g.
We will use the conversion fraction: \(\dfrac{1000 ~mg}{1~g} \)
\(\Large 1.42 \dfrac{\cancel{g}}{cm} \times \dfrac{1000 ~mg}{1~\cancel{g}}\)
As you can see, g cancels out leaving mg.

- mathstudent55

We still need to convert cm to mm.
Since there are 10 mm in a cm, we have a conversion fraction of
\(\dfrac{10~mm}{1~cm}\) and \(\dfrac{1~cm}{10~mm} \)
How do we know which one to use?
\(\Large 1.42 \dfrac{\cancel{g}}{cm} \times \dfrac{1000 ~mg}{1~\cancel{g}}\)
We see that in our problem, cm is in the denominator, so to cancel out cm, we need cm in the numerator of the conversion fraction. that means we need to multiply by \(\dfrac{1~cm}{10~mm} \)
\(\Large 1.42 \dfrac{\color{red}{\cancel{g}}}{\color{blue}{\cancel{cm}}} \times \dfrac{1000 ~mg}{1~\color{red}{\cancel{g}}} \times \dfrac{1~\color{blue}{\cancel{cm}}}{10~mm}\)
Now when you multiply it out, the only units left are mg/mm, and your unit conversion is done.

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