# Nakafa Learning Content

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URL: https://nakafa.com/en/subject/high-school/10/physics/measurement/quantity
Source: https://raw.githubusercontent.com/nakafaai/nakafa.com/refs/heads/main/packages/contents/subject/high-school/10/physics/measurement/quantity/en.mdx

Output docs content for large language models.

---

export const metadata = {
  title: "Physical Quantities",
  description:
    "Learn what a physical quantity is, how base and derived quantities differ, and how quantities connect to SI units and dimensions.",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "04/25/2026",
  subject: "Measurement in Scientific Work",
};

## Reading Quantities from Measurements

When we write a measurement result such as <InlineMath math="0.60 \text{ m}" />, <InlineMath math="2" /> parts are working together.

<BlockMath math="\text{measurement result} = \text{measured value} \times \text{unit}" />

The value <InlineMath math="0.60" /> tells us *how much*. The unit <InlineMath math="\text{m}" /> tells us *which standard it is compared with*. The quantity is the property of an object or event being measured, such as length, mass, time, temperature, or speed.

> Without a quantity, a number has no direction. Without a unit, a number cannot be compared.

## Base and Derived Quantities

In SI, the **International System of Units**, <InlineMath math="7" /> base quantities are used as foundations. Other quantities can be built from combinations of those base quantities.

| Base quantity | Typical symbol | SI unit | Dimension |
| :------------ | :------------- | :------ | :-------- |
| Length | <InlineMath math="\ell,\ x,\ r" /> | <InlineMath math="\text{m}" /> | <InlineMath math="\mathrm{L}" /> |
| Mass | <InlineMath math="m" /> | <InlineMath math="\text{kg}" /> | <InlineMath math="\mathrm{M}" /> |
| Time | <InlineMath math="t" /> | <InlineMath math="\text{s}" /> | <InlineMath math="\mathrm{T}" /> |
| Electric current | <InlineMath math="I" /> | <InlineMath math="\text{A}" /> | <InlineMath math="\mathrm{I}" /> |
| Thermodynamic temperature | <InlineMath math="T" /> | <InlineMath math="\text{K}" /> | <InlineMath math="\Theta" /> |
| Amount of substance | <InlineMath math="n" /> | <InlineMath math="\text{mol}" /> | <InlineMath math="\mathrm{N}" /> |
| Luminous intensity | <InlineMath math="I_v" /> | <InlineMath math="\text{cd}" /> | <InlineMath math="\mathrm{J}" /> |

A derived quantity appears when base quantities are combined. For example, area comes from length multiplied by width.

<BlockMath math="\begin{aligned}
A &= l \times w \\
\text{unit of } A &= \text{m} \times \text{m} = \text{m}^2 \\
\dim A &= \mathrm{L} \times \mathrm{L} = \mathrm{L}^2
\end{aligned}" />

Speed is also a derived quantity because it comes from distance divided by time.

<BlockMath math="\begin{aligned}
v &= \frac{s}{t} \\
\text{unit of } v &= \frac{\text{m}}{\text{s}} = \text{m s}^{-1} \\
\dim v &= \frac{\mathrm{L}}{\mathrm{T}} = \mathrm{L}\mathrm{T}^{-1}
\end{aligned}" />

## Dimension as a Code

Dimension is a compact way to see which base quantities build a quantity. It does not replace units, but it helps us check whether a formula makes sense.

<Mermaid
  chart={`flowchart TD
    A["Choose the measured quantity"] --> B["Identify the base quantities behind it"]
    B --> C["Write the SI unit"]
    B --> D["Write the dimension"]
    C --> E["Check the measurement result"]
    D --> E`}/>

For example, the area of a desk and the area of a sheet of paper can have different values, but they are the same kind of quantity. Both are area, both use the SI unit <InlineMath math="\text{m}^2" />, and both have dimension <InlineMath math="\mathrm{L}^2" />.

On the other hand, length, width, height, diameter, radius, distance, and displacement can all use length units. They all have dimension <InlineMath math="\mathrm{L}" />.

## One Area Calculation

A sheet of paper has length <InlineMath math="0.30 \text{ m}" /> and width <InlineMath math="0.20 \text{ m}" />. Its area is:

<BlockMath math="\begin{aligned}
A &= l \times w \\
&= 0.30 \text{ m} \times 0.20 \text{ m} \\
&= 0.060 \text{ m}^2
\end{aligned}" />

The value <InlineMath math="0.060 \text{ m}^2" /> is the measurement result for area. Since area is built from <InlineMath math="2" /> length quantities, area is a derived quantity.

Notice the pattern: once a unit is built from operations between other units, the quantity is no longer base. This way of reading values, units, and dimensions helps us check whether units and formulas agree.