# Physical quantities and units

> CIE A-Level Physics · CIE 9702 A-Level Physics
> Source: https://www.owlsprep.com/study/cie-9702-u1-overview/
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This foundational unit covers the core language and conventions of physics, from defining quantities to handling measurement uncertainty. These skills are required for every topic in your A-Level Physics course.

**Prerequisites:** GCSE-level understanding of basic measurement and physical quantities

## Learning objectives

- Distinguish between different categories of physical quantities, including scalars and vectors
- Apply SI unit conventions and prefixes correctly to all physical calculations
- Estimate order-of-magnitude values for common physical quantities
- Calculate and combine measurement uncertainties correctly for experimental results

## Unit at a glance

This unit builds the fundamental toolkit you need to work with and communicate physics concepts correctly. We start with how we classify quantities, then move to unit conventions, before covering practical skills like estimation and uncertainty analysis. Every calculation, experiment and problem in the rest of your course relies on the conventions learned here.

This unit is split into 6 connected sub-topics covering theory and practical foundational skills:
- [Types of physical quantity](https://www.owlsprep.com/study/cie-9702-u1-types-of-physical-quantity/) — Learn how we categorize physical quantities for consistent physical analysis.
- [Scalars and vectors](https://www.owlsprep.com/study/cie-9702-u1-scalars-and-vectors/) — Distinguish between scalar and vector quantities, and learn basics of vector combination.
- [SI base and derived units](https://www.owlsprep.com/study/cie-9702-u1-si-base-and-derived-units/) — Understand the SI system, base units, and how to derive units for compound quantities.
- [Unit prefixes](https://www.owlsprep.com/study/cie-9702-u1-unit-prefixes/) — Convert between different magnitudes of units using standard SI prefixes.
- [Estimation of physical quantities](https://www.owlsprep.com/study/cie-9702-u1-estimation-of-physical-quantities/) — Practice estimating the order of magnitude of common everyday physical quantities.
- [Measurement uncertainties](https://www.owlsprep.com/study/cie-9702-u1-measurement-uncertainties/) — Calculate and combine absolute, fractional and percentage uncertainty for experiments.

## Common pitfalls

- **Wrong:** Confusing scalar (magnitude only) and vector (magnitude + direction) quantities.
  - Why it fails: This leads to incorrect calculations when combining quantities, especially in mechanics.
  - Correct: Always explicitly check if a quantity has direction before classifying it.
- **Wrong:** Using mismatched units when substituting values into formulas.
  - Why it fails: Mismatched units lead to drastically incorrect results even if your method is correct.
  - Correct: Convert all quantities to base SI units before starting any calculation.
- **Wrong:** Adding absolute uncertainties when multiplying quantities, or percentage uncertainties when adding.
  - Why it fails: This produces incorrect uncertainty estimates for final experimental results.
  - Correct: Add percentage uncertainties for multiplication/division; add absolute uncertainties for addition/subtraction.

## Cheatsheet

| Concept / Rule | Description |
| --- | --- |
| Scalar quantity | Physical quantity with magnitude only, no direction |
| Vector quantity | Physical quantity with both magnitude and direction |
| SI base units | 7 fundamental units: kilogram (kg), metre (m), second (s), ampere (A), kelvin (K), mole (mol), candela (cd) |
| Order of magnitude | The nearest power of 10 to the value of a physical quantity |
| Percentage uncertainty | $\frac{\text{absolute uncertainty}}{\text{measured value}} \times 100\%$ |
| Combined uncertainty rule | Add % uncertainties for ×/÷; add absolute uncertainties for +/− |

## What's next

Start your study of this unit with the first sub-topic, Types of physical quantity, to build your foundational understanding of how we categorize quantities in physics. Once you complete all sub-topics in this unit, you will move on to the next unit of CIE 9702 A-Level Physics, which covers kinematics, the study of motion.

- [Types of physical quantity](https://www.owlsprep.com/study/cie-9702-u1-types-of-physical-quantity/)
- [Scalars and vectors](https://www.owlsprep.com/study/cie-9702-u1-scalars-and-vectors/)
- [SI base and derived units](https://www.owlsprep.com/study/cie-9702-u1-si-base-and-derived-units/)

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