Units of Measurement

The metric system is built on powers of 10, which makes converting straightforward. Here are the facts you build on this year:

• Length: $10\text{ mm} = 1\text{ cm}$, $100\text{ cm} = 1\text{ m}$, $1000\text{ m} = 1\text{ km}$.
• Mass: $1000\text{ g} = 1\text{ kg}$, $1000\text{ kg} = 1\text{ tonne}$.
• Capacity: $1000\text{ ml} = 1\text{ litre}$.

So $3.6\text{ km} = 3.6 \times 1000 = 3600\text{ m}$, and $940\text{ g} = 940 \div 1000 = 0.94\text{ kg}$.

This year the new challenge is converting area and volume units — and, as you will see next, those do not use the same conversion number.

Here is a fact that surprises many students. There are $100\text{ cm}$ in a metre — but there are not $100\text{ cm}^2$ in a square metre.

Picture a square that is $1\text{ m}$ along each side. That is the same as $100\text{ cm}$ along each side. Its area is $100 \times 100 = 10\,000\text{ cm}^2$.

So the area rule is: square the length conversion factor.

• $1\text{ cm}^2 = 10 \times 10 = 100\text{ mm}^2$
• $1\text{ m}^2 = 100 \times 100 = 10\,000\text{ cm}^2$

Volume units go one step further — you cube the factor, because volume has three dimensions:

• $1\text{ cm}^3 = 10 \times 10 \times 10 = 1000\text{ mm}^3$
• $1\text{ m}^3 = 100 \times 100 \times 100 = 1\,000\,000\text{ cm}^3$

A handy capacity link: $1\text{ cm}^3$ of space holds exactly $1\text{ ml}$, so $1000\text{ cm}^3 = 1\text{ litre}$.

A compound unit is built from two measurements. You meet them constantly — they describe a rate, how one quantity compares to another.

Speed combines distance and time. It is measured in units like kilometres per hour ($\text{km/h}$) or metres per second ($\text{m/s}$): $\text{speed} = \frac{\text{distance}}{\text{time}}.$

The triangle helps you rearrange. Cover the letter you want and read off the rest: cover D and you see $\text{S} \times \text{T}$; cover T and you see $\text{D} \div \text{S}$.

So a car travelling $150\text{ km}$ in $2\text{ hours}$ has a speed of $150 \div 2 = 75\text{ km/h}$.

Density combines mass and volume — how heavy something is for its size. It is measured in units like $\text{g/cm}^3$: $\text{density} = \frac{\text{mass}}{\text{volume}}.$

A block of mass $60\text{ g}$ and volume $20\text{ cm}^3$ has density $60 \div 20 = 3\text{ g/cm}^3$. The word "per" is the clue — it always means "divided by".

Time is the measurement that does not use powers of 10, so you handle it carefully:

• $60\text{ seconds} = 1\text{ minute}$
• $60\text{ minutes} = 1\text{ hour}$
• $24\text{ hours} = 1\text{ day}$

To convert minutes into hours you divide by 60: $90\text{ minutes} = 90 \div 60 = 1.5\text{ hours}$. This matters for speed problems — a journey of "$45$ minutes" is $0.75$ hours, not $0.45$.

To find a duration, count on in friendly steps. From $08{:}50$ to $13{:}25$: count $10$ minutes up to $09{:}00$, then $4$ whole hours to $13{:}00$, then $25$ more minutes — a total of $4$ hours $35$ minutes.

The 24-hour clock counts straight on from $0000$ to $2359$. For a pm time, add $12$ to the hours, so $4{:}15\text{ pm}$ becomes $1615$.

Rulers, scales, jugs and thermometers all use a scale of marks. To read one, first find the value of one small step — count the steps between two numbered marks and divide.

In the scale, $0$ to $50$ has $5$ steps, so one step is $50 \div 5 = 10$. The pointer sits $2$ steps past $100$, reading $120$.

This year you also think about accuracy. No real measurement is perfectly exact, so you choose a sensible degree of accuracy:

• A length of string measured with a ruler might be "$23.4\text{ cm}$, to the nearest millimetre".
• The answer to a circle calculation might be rounded to "$1$ decimal place".

A good rule: an answer should not be more precise than the measurements that went into it. If a side is given as $7\text{ cm}$, an answer of $43.96825\text{ cm}^2$ is falsely precise — round it to something sensible like $44\text{ cm}^2$.

Getting confident with units makes lots of later work smoother:

• Area and volume rely on converting square and cube units correctly.
• Speed, distance and time problems lean directly on compound units.
• Density and rates appear in science as well as maths.
• In everyday life, units run through cooking, travel, sport, shopping and science experiments.

If a measurement question feels tricky later, it is often a unit conversion or an accuracy decision underneath. Come back to this guide whenever you need it — careful unit work pays off everywhere.