A scale of $1:n$ means every $1$ unit on the drawing represents $n$ of the same unit in real life — that's why the ratio has no units of its own, as long as both sides are measured the same way.

1. Convert both parts to the same unit.
2. Write as a ratio and simplify so the drawing side becomes $1$.

Example: $2$ cm represents $3$ km. Convert $3$ km to cm: $3 \times 100{,}000 = 300{,}000$ cm. Ratio: $2:300{,}000$. Divide both sides by 2: $\mathbf{1:150{,}000}$.

Measure the length on the drawing (to the nearest mm), multiply by $n$, then convert the result to a sensible real-world unit.

Example: Scale $1:150{,}000$; measured distance $5.8$ cm.

This is the reverse: convert the real distance to the same unit as the scale, then divide by $n$ (not multiply).

Example: Scale $1:12{,}000$; actual length $125$ m. Convert to cm: $125\times100=12{,}500$ cm. Divide by $n$: $12{,}500\div12{,}000\approx1.04$ cm.

Convert the real-world side into the same unit as the drawing side before simplifying — the same approach as converting a statement scale, just phrased slightly differently.

Example: "1 cm represents 2 m." Convert 2 m to cm: $2\times100=200$ cm. The scale is $1:200$.

Scale drawing and bearings are often combined: first use the scale to convert a measured distance into the true real-life distance, and only then use that distance (plus a protractor-measured angle) to describe the bearing of one location from another. Getting the distance right is the essential first step, since any error there carries forward into the bearing calculation.

A map has scale $1:25{,}000$. Two towns are $6.4$ cm apart on the map. A tourist drives between them by road, and the road distance is actually $1.8$ km longer than the straight-line map distance. Find the road distance in km.

1. Straight-line distance: $6.4 \times 25{,}000 = 160{,}000$ cm.
2. Convert to km: $160{,}000 \div 100{,}000 = 1.6$ km.
3. Road distance: $1.6 + 1.8 = 3.4$ km.