Choose appropriate units of mass

As we have been learning, everything in math that relates to the ‘real world’ has units. If there's a point to it there are units attached to it. The units that we use are particular to what we are measuring.  

There are some units we need to know about formally, and how to convert between them. 

LENGTH/DISTANCE -->  mm, cm, m, km 

AREA  --> mm² , cm², m², km² 

VOLUME --> mm³, cm³, m³, km³

CAPACITY -->  mL, L, kL, ML

WEIGHT (actually called MASS) -->  mg, g, kg, metric ton 

TIME -->  seconds, mins, hrs, days, weeks, months, years 

Mass vs Weight

This is a tricky one!  Colloquially, which means words that we use everyday, we tend to use the word weight when what we mean mathematically is actually called mass.  

Mass is a measurement of how much matter is in an object. The weight is a measurement of how hard gravity is pulling on that object.

Your mass is the same wherever you are, whether you are on Earth, floating around on the moon, or struggling to move on Jupiter (the biggest planet).  This is because wherever you are the amount of stuff you are made of does not change.  

Your weight depends on how much gravity is acting on you at the moment. So that means you would weigh less on the moon than on Earth because the force of gravity is less there, and you would weigh about 2.5 times more on Jupiter because of the greater force of gravity there. 

So when we talk about mass and weight, if we are talking about being here on the earth, then they are pretty much the same thing.  But if we want to look at the physics of a different planet or moon with different gravitational pulls then mass and weight can be very different.  

Units of MASS

Mass is usually measured using one of the following units: 

• milligrams (mg) 
• grams (g) 
• kilograms (kg) 
• metric ton (t) 

You should be used to most of these through previous experiences in measuring your weight, cooking, medicines or even in science experiments you may have done at school. 

$1$1 g = $1000$1000 mg
$1$1 kg = $1000$1000 g = $1000000$1000000 mg ($1000\times1000$1000×1000)
$1$1 t = $1000$1000 kg = $1000000$1000000 g = $1000000000$1000000000 mg 

To move from larger mass units to smaller mass units multiply each step.

To move from smaller mass units to larger mass units divide each step.

Do you see some patterns when looking at changing units of mass? What I see is between each step it is a factor of 1000.  That's different to measurement, but possibly easier to remember!

The prefixes

Notice the similarities with the naming of units here to the units we have used throughout measurement.

The prefix milli.  Milli means $\frac{1}{1000}$11000​th of something.  So we can see here that a milligram was $\frac{1}{1000}$11000​th of a gram, which means that $1000$1000 mg are in $1$1 gram.  That was the same as a millimetre.  where $1000$1000 mm were in $1$1 metre.  

Also the prefix kilo.  Kilo means $1000$1000 of something, so a kilogram is $1000$1000 grams and a kilometre is $1000$1000 metres!

Example

Question 1

Question: Change $3.25$3.25kg into mg. 

Think: Think about the steps needed to move from kg to mg.  (kg-> g-> mg) and identify the multiplicative amounts for each step.  I suggest moving through each step one part at a time.

Do:  First convert to grams $3.25\times1000$3.25×1000 g = $3250$3250 g

Then convert to mg  $3250\times1000$3250×1000 mg = $3250000$3250000 mg

It really doesn't matter if you think about it like I did, or if you do something different.  What is important is to keep track of your steps. See how my units changed as I was making the changes.  

Here is another:

question 2

Question: Convert $148960000$148960000 mg into tonnes

Think: Think about the steps needed to move from mg to tonnes.  (mg -> g -> kg  -> t) and identify the division amounts for each step. 

Do: First convert to grams  $148960000\div1000=148960$148960000÷​1000=148960 g

Now convert to kilograms  $148960\div1000=148.96$148960÷​1000=148.96 kg

And then finally into tonnes  $148.96\div1000$148.96÷​1000 = $0.14896$0.14896 t