Changing units
A recipe for your science fair project calls for "350 g of flour", but the balance in your classroom reads in kilograms. A test-track data sheet gives a car's speed in km/h, but your 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 closet in Bruno's room is $2\ \text{m}$ high. Express this height in centimeters.
The closet in Bruno's room is $2\ \text{m}$ high. Express this height in centimeters.
A package of rice weighs $2\ \text{kg}$. How many grams is that?
A package of rice weighs $2\ \text{kg}$. How many grams is that?
An old bridge restricts crossing to $3\ \text{t}$. A loaded van weighs $2800\ \text{kg}$, as shown in the figure. Can it cross? Justify your answer by converting both…
An old bridge restricts crossing to $3\ \text{t}$. A loaded van weighs $2800\ \text{kg}$, as shown in the figure.
Can it cross? Justify your answer by converting both masses to the same unit.
Time and capacity
The movie Sophia watched yesterday lasted $1.5\ \text{h}$. How many minutes is that?
The movie Sophia watched yesterday lasted $1.5\ \text{h}$. How many minutes is that?
A bottle of water contains $1.5\ \text{L}$. How many milliliters is that?
A bottle of water contains $1.5\ \text{L}$. How many milliliters is that?
A drink can contains $330\ \text{cm}^3$. a) How many milliliters is that? b) And how many liters?
A drink can contains $330\ \text{cm}^3$. a) How many milliliters is that? b) And how many liters?
Area and volume: beware of squares and cubes!
A fish tank contains $12\ \text{L}$ of water. How many cubic centimeters is that? Remember: $1\ \text{L} = 1000\ \text{cm}^3$.
A fish tank contains $12\ \text{L}$ of water. How many cubic centimeters 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 centimeters 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 centimeters 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 centimeters? b) And in square meters? 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 centimeters? b) And in square meters? c) How many tiles are needed to cover $1\ \text{m}^2$?
A tanker truck carries $20\,000\ \text{L}$ of milk, like the one in the figure. a) How many cubic meters is that? Hint: $1\ \text{m}^3 = 1000\ \text{L}$. b) If the milk…
A tanker truck carries $20\,000\ \text{L}$ of milk, like the one in the figure.
- a) How many cubic meters is that? Hint: $1\ \text{m}^3 = 1000\ \text{L}$. b) If the milk is packaged into bottles of $2\ \text{L}$, how many bottles are filled?
An inflatable pool is box-shaped, $2\ \text{m}$ long, $1\ \text{m}$ wide, and $0.5\ \text{m}$ high, like the one in the figure. a) Calculate its volume in cubic meters.…
An inflatable pool is box-shaped, $2\ \text{m}$ long, $1\ \text{m}$ wide, and $0.5\ \text{m}$ high, like the one in the figure.
- a) Calculate its volume in cubic meters. b) Convert it into liters knowing that $1\ \text{m}^3 = 1000\ \text{L}$. c) If it is filled using a hose that pumps $20\ \text{L}$ per minute, how many minutes does it take to fill?
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 meters per second is the cheetah moving at?
A car travels along the divided highway at $90\ \text{km/h}$, as shown in the figure. Convert its speed into meters per second by dividing by $3.6$.
A car travels along the divided highway at $90\ \text{km/h}$, as shown in the figure.
Convert its speed into meters 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 airplane flies at $900\ \text{km/h}$. a) Convert its speed into meters per second. b) How many meters does it travel in $10\ \text{s}$? c) And in one minute? Express…
An airplane flies at $900\ \text{km/h}$. a) Convert its speed into meters per second. b) How many meters does it travel in $10\ \text{s}$? c) And in one minute? Express this last result in kilometers as well.
Back to the beginning: For the $350\ \text{g}$ of flour in the recipe, you change to kilograms by dividing by $1000$ ($350 \div 1000 = 0.35\ \text{kg}$); if the test-track data sheet shows $72\ \text{km/h}$, in the physics problem you divide by $3.6$ to get $20\ \text{m/s}$. And the cheetah: $108 \div 3.6 = 30\ \text{m/s}$, which is faster than the gazelle's $28\ \text{m/s}$.