Lesson Guide
Explanation
A scale drawing is a similar figure, shrunk by a fixed scale factor. The scale is written as a ratio, one to n. One to one hundred means that one centimetre on the plan stands for one hundred centimetres in real life, which is one metre. The units on both sides of the ratio are the same, so there are no units written in it. The living room on this plan is four point five centimetres long, so in real life it is four point five times one hundred centimetres, which is four point five metres.
Your Turn
On a 1 : 50 plan, a bench is 3 cm long. Check: 3 × 50 = 150 cm = 1.5 m.
Watch Out
1 : 100 does not mean 1 cm stands for 100 m. Both numbers are in the same unit: 100 cm, which is 1 m.
Explanation
Map scales use big numbers, so you need to convert units. There are one hundred centimetres in a metre and one thousand metres in a kilometre, so there are one hundred thousand centimetres in a kilometre. On a one to fifty thousand map, one centimetre stands for fifty thousand centimetres. Divide by one hundred to get metres: five hundred metres. On a one to twenty five thousand map, one centimetre stands for two hundred and fifty metres.
Your Turn
What does 1 cm stand for on a 1 : 10 000 map? Check: 10 000 cm = 100 m.
Watch Out
50 000 cm is 500 m, not 5 km and not 50 m. Divide by 100 for metres, then by 1000 more for kilometres.
Explanation
To turn a map distance into a real distance, multiply by the scale number, then convert. On a one to two hundred thousand map, two towns are six point five centimetres apart. Six point five times two hundred thousand is one million three hundred thousand centimetres. Divide by one hundred to get thirteen thousand metres, and by one thousand again to get thirteen kilometres.
Your Turn
Map scale 1 : 120 000, map distance 4 cm. Check: 4 × 120 000 = 480 000 cm = 4.8 km.
Watch Out
Convert the whole answer. 1 300 000 cm is 13 km, not 130 km: count the zeros, or go cm → m → km in two steps.
Explanation
Going the other way, from real life to the map, you divide by the scale number. Convert the real distance into centimetres first, so both parts of the ratio are in the same unit. Twelve kilometres is twelve thousand metres, which is one million two hundred thousand centimetres. Divide by three hundred thousand: the map distance is four centimetres. A map length should be small, so if you get a huge number, you multiplied when you should have divided.
Your Turn
On a 1 : 70 000 map, how long is a 2.1 km road? Check: 210 000 cm ÷ 70 000 = 3 cm.
Watch Out
Divide, do not multiply, and convert km to cm before you divide. 12 ÷ 300 000 gives a tiny number in km, not 4 cm.
Explanation
Sometimes you know a map length and the real length it stands for, and you need the scale. Here five centimetres stands for one point five kilometres. Write both in centimetres: one point five kilometres is one hundred and fifty thousand centimetres. So the ratio is five to one hundred and fifty thousand. Divide both parts by five to make the first part one: the scale is one to thirty thousand. This is also how you read a scale bar.
Your Turn
8 cm on a plan stands for 4 m. Check: 4 m = 400 cm, and 8 : 400 = 1 : 50.
Watch Out
Divide by the map length too. 1.5 km = 150 000 cm, but the scale is not 1 : 150 000, because that was 5 cm, not 1 cm. Quiz and exercises now.
📌 Key Points — this lesson in a nutshell
- A scale 1 : n means 1 unit on the drawing stands for n of the same unit in real life.
- Convert with 100 cm = 1 m and 1000 m = 1 km, so 100 000 cm = 1 km. On 1 : 50 000, 1 cm is 50 000 cm = 500 m.
- Map → real: multiply by n. Real → map: divide by n. Put both lengths in cm first.
- To find a scale, write map length : real length in the same unit, then divide both by the map length to get 1 : n.
- A scale bar is a picture of the scale: measure it, then write it as 1 : n.
Step 1: Introduction
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