Standard & Compound Units Flashcards

All 31 cards in this deck

How many seconds are in a minute, minutes in an hour and hours in a day?

60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day.

How do you write a pm time using the 24-hour clock?

e.g. 6.45 pm

Add 12 to the hours: 18 45.
(12 noon stays 12 00; 12.30 am is 00 30.)

What are the steps to write a number of minutes as hours and minutes?

e.g. 140 minutes

1. Divide by 60 for the whole hours: $140 \div 60 = 2$ remainder 20
2. The remainder is the minutes: 20
3. Answer: 2 hours 20 minutes

True or false? 1 hour 18 minutes written as a decimal number of hours is 1.18 hours.

False.
It is 1.3 hours, because $18 \div 60 = 0.3$.

What are the steps to find how long it is between two clock times?

e.g. from 07:22 to 09:00

1. Count on to the next whole hour: 07:22 to 08:00 is 38 minutes
2. Count on the whole hours: 08:00 to 09:00 is 1 hour
3. Add them: 1 hour 38 minutes (= 98 minutes)

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

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

What are the metric conversions for mass between g, kg and tonnes?

1000 g = 1 kg, 1000 kg = 1 tonne.

What are the conversions between ml, litres and cm³?

1 ml = 1 cm$^3$, 1000 ml = 1 litre, so 1000 cm$^3$ = 1 litre.

When converting units, when do you multiply and when do you divide?

Multiply when changing to a smaller unit, divide when changing to a larger unit.
e.g. m to mm: $\times 1000$; cm to m: $\div 100$.

True or false? To change a mass in grams into kilograms you multiply by 1000.

False.
You divide by 1000, because a kilogram is the larger unit.

What are the steps to change a speed in metres per second into kilometres per hour?

e.g. 30 m/s

1. Multiply by 3600 for metres per hour: $30 \times 3600 = 108\,000$
2. Divide by 1000 for km per hour: $108\,000 \div 1000 = 108$
3. Answer: 108 km/h (or just multiply by 3.6)

How many mm² are there in 1 cm²?

100 mm$^2$, because $10 \times 10 = 100$.

How many cm² are there in 1 m²?

10 000 cm$^2$, because $100 \times 100 = 10\,000$.

How many cm³ are there in 1 m³?

1 000 000 cm$^3$, because $100 \times 100 \times 100 = 1\,000\,000$.

How many mm³ are there in 1 cm³?

1000 mm$^3$, because $10 \times 10 \times 10 = 1000$.

True or false? To change an area from m² into cm² you multiply by 100.

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

What are the steps to change a volume in cm³ into m³?

e.g. 8000 cm³

1. Find the length factor: 100 cm = 1 m
2. Cube it for volume: $100^3 = 1\,000\,000$
3. Divide (m$^3$ is larger): $8000 \div 1\,000\,000 = 0.008$ m$^3$

What is a compound measure?

A measure made from two other units divided by one another.
e.g. speed (distance per unit time), density, pressure, rate of pay.

What does 'time and a half' mean for an hourly rate of pay?

Each overtime hour is paid at $1.5 \times$ the normal hourly rate.
e.g. £12 per hour becomes £18 per hour.

What are the steps to work out a day's pay when overtime is paid?

e.g. 10 hours worked, £12 per hour, overtime at $1\frac{1}{4}$ times after 8 hours

1. Pay for normal hours: $12 \times 8 = £96$
2. Overtime hours and rate: $10 - 8 = 2$ hours at $1.25 \times 12 = £15$
3. Add: $96 + 2 \times 15 = £126$

What is the formula for flow rate?

Flow rate = volume $\div$ time.
e.g. measured in litres per minute or cm$^3$ per second.

What must you check about the units before using a compound measure formula?

e.g. mass 12.5 kg with density in g/cm³

The units must match the formula's units — convert first: $12.5$ kg $= 12\,500$ g, giving a volume in cm$^3$.

What is the formula for speed?

Speed = distance $\div$ time.

True or false? Average speed is the total distance divided by the total time.

True.
It is not the average of the separate speeds.

What is the formula for density?

Density = mass $\div$ volume.
e.g. measured in g/cm$^3$ or kg/m$^3$.

What is the formula for pressure, and how do you find force or area from it?

Pressure = force $\div$ area; force = pressure $\times$ area; area = force $\div$ pressure.

True or false? $1\text{ m}^3$ of water is the same as 1000 litres.

True. $1\text{ m}^3 = 1\,000\,000\text{ cm}^3$ and $1000\text{ cm}^3 = 1$ litre, so $1\text{ m}^3 = 1000$ litres.

What are the steps to find the time for a journey from its distance and average speed?

e.g. 36 km at an average speed of 16 km/h

1. Time $=$ distance $\div$ speed: $36 \div 16 = 2.25$ hours
2. Multiply the decimal part by 60: $0.25 \times 60 = 15$ minutes
3. Write the answer: 2 hours 15 minutes

What is the formula for distance when you know the average speed and the time?

e.g. 55 mph for 2 hours

Distance $=$ speed $\times$ time.

e.g. $55 \times 2 = 110$ miles

What are the steps to find the density of a drink made by mixing two liquids of different densities?

e.g. 20 cm³ of syrup at 1.4 g/cm³ mixed with 80 cm³ of water at 1 g/cm³

1. Mass of each $=$ density $\times$ volume: $20 \times 1.4 = 28$ g and $80 \times 1 = 80$ g
2. Add for the totals: mass $= 108$ g, volume $= 100$ cm³
3. Density $=$ total mass $\div$ total volume: $108 \div 100 = 1.08$ g/cm³

True or false? When two liquids of different densities are mixed, the density of the mixture is the mean of the two densities.

False. You must work out the total mass and the total volume, then divide: density $=$ total mass $\div$ total volume.