Question

If you were asked to convert 25 kg to the unit mg, what would be the first fraction used in the conversion?

Answer 1

First off, what might you want to do? Convert kilograms to grams since you can easily convert between grams and anything else. Kilograms to miligrams directly would just be confusing.

So let's think about this, we need to convert kg to g. How many grams are in a kilogram? There are 1,000 grams in a kilogram. So what we're doing is saying that

1,000g/1kg is a conversion factor since it's saying 1,000g per 1kg. You can also look at it the other way, 1kg/1000g since for every 1 kg you have 1,000g. Since it's converting, it's kind of like multiplying any number by one, since it doesn't change the value, it just changes the units. So how do we decide which is right of the two to use for conversion?

Consider multiplying them together, the number times the conversion, and that the units are now no longer just useless things tacked on the ends of numbers but are actually variables that you can do algebra with! Sounds scarier than it really is, but here, take a look at this and it'll be obvious:

25kg*1000g/1kg or 25kg*1kg/1000g?

In the first one, you see that you have kg in the numerator and denominator, so it cancels out like x/x would, leaving you with the units of g! On the other side you end up with kg^2/g which doesn't make any sense, so you can tell that that must be wrong.

All you're doing is making sure that you have kg on top and kg on bottom so that they divide out to be 1. The only other thing you need to consider is that a kilogram is huge and gram is small, so there must be more grams than kilograms, and you can write it as 1000g/1kg!

I hope that helps, if you need more clarification I'd be happy to help!

Answer 2

Thank yoou! that helped me so much!

Answer 3

You're welcome, don't forget to give medals when you get good answers!