Measuring, Estimating and Units

Hong Kong

Stage 1 - Stage 3

Lesson

As we have been learning, everything in maths 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 --> *mm ^{2} , cm^{2}, m^{2}, km^{2} *

VOLUME -->* mm ^{3}, cm^{3}, m^{3}, km^{3}*

CAPACITY --> *mL, L, kL, ML*

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

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

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.

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!

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}$11000th of something. So we can see here that a milligram was $\frac{1}{1000}$11000th 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!

**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

Recall

When multiplying by powers of 10, the digits in the number all move to the right.

So when multiplying by 1000 move the digits 3 places to the right.

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**: 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