Changing units
A recipe says "350 g of flour", but the only scales at home show kilograms. On a journey, the GPS shows speed in km/h, but the physics problem needs it in m/s. Changing units without changing the real quantity is one of the most widely used tools in science and in everyday life.
The conversion factor
The wardrobe in Bruno's room is $2\ \text{m}$ high. Express this height in centimetres.
The wardrobe in Bruno's room is $2\ \text{m}$ high. Express this height in centimetres.
A fun run has a route of $5\ \text{km}$. How many metres is that?
A fun run has a route of $5\ \text{km}$. How many metres is that?
Leo's ruler measures $30\ \text{cm}$, like the one in the figure. How many millimetres is that? And how many metres?
Leo's ruler measures $30\ \text{cm}$, like the one in the figure.
How many millimetres is that? And how many metres?
Time and capacity
The film Nerea watched yesterday lasted $1,5\ \text{h}$. How many minutes is that?
The film Nerea watched yesterday lasted $1,5\ \text{h}$. How many minutes is that?
A bottle of water contains $1,5\ \text{L}$. How many millilitres is that?
A bottle of water contains $1,5\ \text{L}$. How many millilitres is that?
Break time lasts $30\ \text{min}$. How many seconds is that?
Break time lasts $30\ \text{min}$. How many seconds is that?
Area and volume: beware of squares and cubes!
A fish tank contains $12\ \text{L}$ of water. How many cubic centimetres is that? Remember: $1\ \text{L} = 1000\ \text{cm}^3$.
A fish tank contains $12\ \text{L}$ of water. How many cubic centimetres is that? Remember: $1\ \text{L} = 1000\ \text{cm}^3$.
The floor of Julia's room has an area of $12\ \text{m}^2$. a) How many square centimetres is that? Note: $1\ \text{m}^2$ is not $100\ \text{cm}^2$. b) Explain in words…
The floor of Julia's room has an area of $12\ \text{m}^2$. a) How many square centimetres is that? Note: $1\ \text{m}^2$ is not $100\ \text{cm}^2$. b) Explain in words (or with a drawing of a square with a side of $1\ \text{m}$) why $1\ \text{m}^2 = 10\,000\ \text{cm}^2$. The square in the figure may help you:
A square tile has sides of $50\ \text{cm}$, as shown in the figure. a) What is its area in square centimetres? b) And in square metres? c) How many tiles are needed to…
A square tile has sides of $50\ \text{cm}$, as shown in the figure.
- a) What is its area in square centimetres? b) And in square metres? c) How many tiles are needed to cover $1\ \text{m}^2$?
Speed: km/h and m/s
A cheetah runs at $108\ \text{km/h}$ and a gazelle covers $28\ \text{m}$ in a single second: because the units are different, we cannot tell at a glance which is faster, so how many metres per second is the cheetah moving at?
A car travels along the dual carriageway at $90\ \text{km/h}$, as shown in the figure. Convert its speed into metres per second by dividing by $3,6$.
A car travels along the dual carriageway at $90\ \text{km/h}$, as shown in the figure.
Convert its speed into metres per second by dividing by $3,6$.
A sprinter runs at $10\ \text{m/s}$. Express his speed in $\text{km/h}$ by multiplying by $3,6$.
A sprinter runs at $10\ \text{m/s}$. Express his speed in $\text{km/h}$ by multiplying by $3,6$.
An aeroplane flies at $900\ \text{km/h}$. a) Convert its speed into metres per second. b) How many metres does it travel in $10\ \text{s}$? c) And in one minute? Express…
An aeroplane flies at $900\ \text{km/h}$. a) Convert its speed into metres per second. b) How many metres does it travel in $10\ \text{s}$? c) And in one minute? Express this last result in kilometres as well.
Back to the beginning: For the $350\ \text{g}$ of flour in the recipe, you change to kilograms by dividing by $1000$ ($350 : 1000 = 0{,}35\ \text{kg}$); and if the GPS shows $90\ \text{km/h}$, in the physics problem you divide by $3{,}6$ to get $25\ \text{m/s}$.