Standard & Compound Units Flashcards

All 31 cards in this deck

How do you convert a number of minutes into hours?

e.g. 78 minutes

Divide by 60.
$78 \div 60 = 1.3$ hours

How many seconds are there in one hour?

$3600$, since $60 \times 60 = 3600$.

True or false? A time of $2.75$ hours is 2 hours 75 minutes.

False. $0.75 \times 60 = 45$, so it is 2 hours 45 minutes.

How is 2:45 pm written as a 24-hour time?

14 45

What are the steps to find how long a journey lasts from its two 24-hour times?

e.g. 13 30 to 14 48

1. Count on to the next whole hour: 13 30 to 14 00 is 30 min
2. Count on to the finish: 14 00 to 14 48 is 48 min
3. Add: $30 + 48 = 78$ min $=$ 1 hour 18 minutes

When working out a speed in km/h, what must you do with a time given in hours and minutes?

e.g. 1 hour 18 minutes

Change it into hours as a decimal: $1 + 18 \div 60 = 1.3$ hours.

What are the metric conversions between mm, cm, m and km?

$1$ cm $= 10$ mm, $1$ m $= 100$ cm, $1$ km $= 1000$ m

What are the metric conversions for mass between grams, kilograms and tonnes?

$1$ kg $= 1000$ g, $1$ tonne $= 1000$ kg

How many millilitres are there in 1 litre?

$1000$ ml. Also $1$ centilitre $= 10$ ml.

When you convert a measurement into a smaller unit, do you multiply or divide?

e.g. 3.2 kg into grams

Multiply, as there are more of the smaller unit.
$3.2 \times 1000 = 3200$ g

True or false? To change 4500 g into kilograms you multiply by 1000.

False. You divide by 1000, giving $4.5$ kg.

How many square centimetres are there in $1\ \text{m}^2$?

$10\,000$, since $100^2 = 10\,000$.

How many square millimetres are there in $1\ \text{cm}^2$?

$100$, since $10^2 = 100$.

How many cubic centimetres are there in $1\ \text{m}^3$?

$1\,000\,000$, since $100^3 = 1\,000\,000$.

How many cubic millimetres are there in $1\ \text{cm}^3$?

$1000$, since $10^3 = 1000$.

What is the link between litres, cubic centimetres and cubic metres?

$1$ litre $= 1000\ \text{cm}^3$, so $1\ \text{m}^3 = 1000$ litres.

True or false? To convert an area from $\text{m}^2$ into $\text{cm}^2$ you multiply by 100.

False. You multiply by $100^2 = 10\,000$.

What are the steps to convert a speed in km/h into m/s?

e.g. 180 km/h

1. Multiply by 1000 to change km into m: $180 \times 1000 = 180\,000$ m/h
2. Divide by 3600 to change per hour into per second: $180\,000 \div 3600 = 50$ m/s

How do you convert a density in $\text{g/cm}^3$ into $\text{kg/m}^3$?

e.g. $2.5\ \text{g/cm}^3$

Multiply by 1000: $2.5\ \text{g/cm}^3 = 2500\ \text{kg/m}^3$.

How do you convert a rate of pay in £ per hour into £ per minute?

e.g. £12 per hour

Divide by 60: £12 per hour $=$ £0.20 per minute.

What are the steps to find the mass of a solid from its density?

e.g. a cuboid 2 cm by 3 cm by 4 cm made of metal of density $5\ \text{g/cm}^3$

1. Find the volume: $2 \times 3 \times 4 = 24\ \text{cm}^3$
2. Use mass $=$ density $\times$ volume: $5 \times 24 = 120$ g

What are the steps to find the density of a mixture of two liquids?

e.g. $80\ \text{cm}^3$ of density $1.8\ \text{g/cm}^3$ mixed with $40\ \text{cm}^3$ of density $1.2\ \text{g/cm}^3$

1. Mass of each: $1.8 \times 80 = 144$ g and $1.2 \times 40 = 48$ g
2. Totals: mass $192$ g, volume $120\ \text{cm}^3$
3. Density $= 192 \div 120 = 1.6\ \text{g/cm}^3$

How do you find the time taken to fill a container from its volume and the rate of flow?

e.g. a $3000\ \text{cm}^3$ tank filled at $250\ \text{cm}^3$ per second

Time $=$ volume $\div$ rate of flow: $3000 \div 250 = 12$ seconds.

What is the formula for speed?

speed $=$ distance $\div$ time.
So distance $=$ speed $\times$ time and time $=$ distance $\div$ speed.

What is the formula for density?

density $=$ mass $\div$ volume.
So mass $=$ density $\times$ volume and volume $=$ mass $\div$ density.

What is the formula for pressure, and what units is it measured in?

pressure $=$ force $\div$ area, measured in newtons/$\text{m}^2$ (force in newtons, area in $\text{m}^2$).

What are the steps to find the average speed for a journey made of two stages?

e.g. 40 km in 1 hour, then 20 km in 30 minutes

1. Total distance: $40 + 20 = 60$ km
2. Total time in consistent units: $1 + 0.5 = 1.5$ hours
3. Average speed $=$ total distance $\div$ total time $= 60 \div 1.5 = 40$ km/h

True or false? If one stage of a journey is driven at 80 km/h and the next at 60 km/h, the average speed for the whole journey is 70 km/h.

False. Average speed $=$ total distance $\div$ total time; the mean of the speeds only works if the two stages take the same time.

True or false? Mixing a liquid of density $70\ \text{kg/m}^3$ with a liquid of density $280\ \text{kg/m}^3$ gives a mixture of density $350\ \text{kg/m}^3$.

False. Densities cannot be added; find the total mass and total volume, then divide.

What is the formula for pressure?

$\text{pressure} = \dfrac{\text{force}}{\text{area}}$

e.g. force in newtons and area in $\text{m}^2$ gives pressure in $\text{N/m}^2$

What are the steps to find the area of the face in contact from the force and the pressure?

e.g. a box exerting a force of 180 newtons at a pressure of 90 $\text{N/m}^2$

1. Start from $\text{pressure} = \dfrac{\text{force}}{\text{area}}$
2. Rearrange: $\text{area} = \dfrac{\text{force}}{\text{pressure}}$
3. Substitute: $180 \div 90 = 2\ \text{m}^2$