Measuring, Estimating and Units

Hong Kong

Stage 1 - Stage 3

Lesson

In all our years of learning maths, we've learnt how to make all kinds of calculations. However, if I told you the answer is $42$42, your initial response may be, "$42$42 what?" That's why units of measurement are really important!

We can use units of measurement to define any physical phenomenon, such as quantities, weights, lengths, areas, volumes and rates. Let's look at some different units of measurement now.

Length (distance) is a measurement of one dimension. For example, we could measure from one point to another

Units of measurements for length include millimetres ($mm$`m``m`), centimetres ($cm$`c``m`), metres ($m$`m`) and kilometres ($km$`k``m`).

Area is a measure of two dimensions: length and width. Hence, it is measured in square units.

Units of measurements for area include square millimetres ($mm^2$`m``m`2), square centimetres ($cm^2$`c``m`2), square metres ($m^2$`m`2) and hectares ($ha$`h``a`).

Volume is a measure of three dimensions: length, width and height. Hence, it's measured in cubed units.

Units of measurements for volume include millimetres cubed ($mm^3$`m``m`3), centimetres cubed ($cm^3$`c``m`3), metres cubed ($m^3$`m`3)

Measurements of Mass

Units of measurement for mass include grams (g), kilograms (kg) and tonnes (t).Mass is a measure of how heavy something. We often refer to the mass of an object as its weight.

Capacity is a measure of how much something holds, such as how much liquid will fit in a bottle.

Measures of capacity include millilitres (ml) and litres (l).

A rate is a ratio between two measurements with different units. There are any number of combinations of measurement units for rates, such as dollars per kilogram ($/kg), kilometres per hour (km/h) and so on.

Any formula whose components are measurements will have units attached to each of the pronumerals.

Here is a formula we a familiar with, the speed of an object is a measure of the distance traveled per unit of time.

$S=\frac{d}{t}$`S`=`d``t`

The units for Speed in the formula are derived from the units used for distance and time. So if the distance is measured in kilometres and time is measured in hours, then the

$\text{Speed (unit) }=\frac{\text{distance (units) }}{\text{time (unit) }}$Speed (unit) =distance (units) time (unit)

$\text{Speed (unit) }=\frac{\text{kilometres }}{\text{hour }}$Speed (unit) =kilometres hour

$\text{Speed (unit) }=\text{kilometres / hour }$Speed (unit) =kilometres / hour

The area of a rectangle is given by $A=l\times w$`A`=`l`×`w`, where $l$`l` is the length and $w$`w` is the width. Both length and width must be of the same units when performing the multiplication to find the area.

What would the unit for area be if the length and width are in millimeters?

m

^{2}Acm-km

Bmm

^{2}Cmm

D

Adam plotted a point to represent material purchases ($x$`x`) and the costs involved ($y$`y`). When Adam bought $140$140cm of material, it cost $\$2.20$$2.20.

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What unit is the $x$

`x`-axis using?cost in dollars of material purchased per meter

Acost in dollars of material purchased per sale

Bmeters of material purchased

Ccentimeters of material purchased

DWhat unit is the $y$

`y`-axis using?cost in dollars of material purchased

Acentimeters of material purchased

Bcost in cents of material purchased

Cmeters of material purchased

D