Units of measure are used for measuring and comparing physical quantities like length, weight and volume. This skill helps us with everyday tasks, such as converting metric and imperial units. Different units of measurement include kilometres, miles, grams and ounces.
This GCSE Maths revision guide explains the key aspects of measurement units, focussing on standard units. Examples and quiz questions are included to test your understanding. If you need further support, TeachTutti has DBS-checked and experienced GCSE Maths tutors who can help you learn about and revise units of measurement.
Metric units and imperial units
Standard units of measure are all around us. They provide information about the object, including length, weight, area, volume and time. There are two main systems. The metric system of units is the international system of units, which is used globally - these units are called SI units. There is also the imperial system, used by countries including the US and the UK:
- Metric units: The metric system is better for calculations because it is numerical based. There are seven SI base units: kilogram (kg) to measure mass, meter (m) to measure length, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) to measure the amount of substance and condela (cd) for luminous intensity.
- Imperial units: Inches, feet and miles are used for length. Pounds (lb) and ounces (oz) are used for weight. This system has historical usage and is more suitable in certain situations.
As an example, let's try to measure the length of a football pitch. The length is 100 metres. This can be written as 0.1 kilometres in metric or 328 feet in imperial.
1
Which is a metric unit of length?
Converting systems of units
We often need to convert units of measure in GCSE examinations and everyday life. This calculation requires using conversion factors to write a quantity in different units. This allows us to standardise quantities and compare them effectively when solving problems:
- Converting in the same system: To convert within metric units, multiply or divide by powers of 10. For example, 1 metre = 100 centimetres. To turn 3 metres into centimetres, we need to multiply 3 by 100 (3 × 100 = 300 cm).
- Converting between systems: Use specific conversion factors to switch between metric and imperial units. For example, 1 inch = 2.54 cm. To convert 12 inches into centimetres, we must multiply 12 by 2.54 (12 × 2.54 = 30.48 cm).
2
1 kilometre is the same as 0.621 miles. How many miles are in 5 kilometres?
Practical applications of Units of Measure
Using a system of measurement is crucial for practical tasks. The reasons can be as diverse as using weights and measures to bake a cake, build a table, or plan a journey. They allow us to accurately measure and convert units. Here are some common real-life scenarios:
- Cooking and baking: We often need to convert between metric (grams) and imperial systems (ounces) when using recipes. For example, if a recipe needs 500 grams of flour, you can convert it to 17.64 ounces.
- Travel: Calculating distance often means switching between miles and kilometres, especially when you are on holiday. Road signs may use miles, while many car manuals use kilometres.
- DIY projects: There's usually a range of units used when working with tools and materials in a DIY project at home. They are often in different systems. For example, a ruler uses both centimetres and inches so you can follow instructions with either system.
3
A recipe needs 2.5 cups of flour. 1 cup equals approximately 240 millilitres. How many millilitres of flour is this?
Challenges with Units of Measure
Units of measure can be confusing when we need to convert between systems or compound units. Here are some common issues and solutions:
- Mixing systems: Problems often use metric and imperial systems, which means converting one of more of the units. A common example is converting miles to kilometres or pounds to kilograms. Use a calculator if permitted for accuracy.
- Compound units: Speed, density and pressure use multiple measurements. For example, density may use grams per cubic centimetre. Process each unit separately before you combine them.
- Decimals and fractions: Working with decimals in metric conversions or fractions in imperial can be tricky. It's a good idea to turn everything into one format to simplify calculations, such as decimals.
Example: Convert compound units
A car is travelling at 60 miles per hour. What is this in metres per second?
- Convert miles to metres: 1 mile = 1,609.34 metres. This means 60 × 1,609.34 = 96,560.4 metres.
- Convert hours to seconds: 1 hour = 3,600 seconds.
- Divide both values: 96,560.4 ÷ 3,600 = 26.82 metres per second.
4
A substance has a density of 8 g/cm³. What is its density in kg/m³?
Tips to master Units of Measure
It goes without saying that practice will give you a strong understanding of units of measure. There are also key strategies that can help you with even the most challenging questions:
- Memorise conversion factors: Try to remember the common conversions e.g. 1 inch = 2.54 cm and 1 litre = 1,000 ml. This saves time and reduces errors.
- Unit cancellation: When converting, arrange the factors so the units are cancelled out during your workings. For example, if you are converting 5 km to metres: 5 × 1,000?m / 1 km = 5,000 m.
- Check your units: Double-check that your answer uses the correct units. Check if the question requires metric or imperial units.
- Practice with real-life problems: Use scenarios like fuel efficiency (miles per gallon to litres per 100 km) or buying material (yards to metres).
- Break down compound units: Complex units have multiple measures. Start by processing one unit at a time before combining them.
5
How many millilitres are in 2.5 litres?
Conclusion - Units of measurements
Understanding units of measure is a practical skill that has many real-world uses beyond GCSE Maths. From converting lengths and volumes to working with compound units like speed or density, we can solve problems easily and accurately with a clear understanding of units. We recommend memorising the common conversions covered in this article, which - combined with logical steps and practice - will help you solve even complex questions.
If you want to test your understanding of this topic, MathsGenie has units and conversion worksheets. If you need further support, TeachTutti has qualified GCSE Maths tutors who can teach in-person or online. Every tutor has an enhanced DBS check.
This post was updated on 30 Nov, -0001.