These questions move between a small measurement on a map, plan or model and the corresponding real measurement. The arithmetic is short, but the direction of scaling and the centimetre, metre or kilometre conversion must both be correct.
Use the scale in the right direction
Read 1:n as one drawing unit to n real units. Label the two sides before calculating. For drawing to reality, multiply by n because the real object is larger. For reality to drawing, first express the real length in the drawing unit, usually centimetres, then divide by n. Convert the result only when the requested unit differs.
| Direction | Form | Tiny example |
|---|---|---|
| Drawing to reality | real length in the same unit equals drawing length times n | At 1:400, 7.5 centimetres represents 3,000 centimetres, which is 30 metres. |
| Reality to drawing | drawing length equals real length in the same unit divided by n | At 1:125, 11.25 metres becomes 1,125 centimetres, then 1,125 divided by 125 gives 9 centimetres. |
| Check the result | Multiply the drawing length by n and recover the real length in matching units. | A 9-centimetre drawing length at 1:125 checks back to 1,125 centimetres in reality. |
Metric conversions are separate from the scale. One metre is 100 centimetres, and one kilometre is 100,000 centimetres. Write the intermediate unit explicitly. A realistic direction check also helps: a model measurement should be smaller than the corresponding real measurement when n is greater than one.
Reject the tempting wrong routes
| Tempting route | How to reject it |
|---|---|
| Keep the scaled digits but relabel centimetres as kilometres or metres. | The scale multiplication does not convert units. Write the result in centimetres first, then use the metric conversion. |
| Move the decimal point one place too far or not far enough. | Use explicit division by 100 or 100,000. Then multiply back to centimetres to verify the conversion. |
Try it
A room plan uses scale 1:100. A sofa is 2.4 metres long in reality. How long is it on the plan? Enter the number of centimetres.
Which scale calculations are correct? Select all that apply.
- At 1:50,000, 4 centimetres on a map represents 2 kilometres.
- At 1:200, 3.5 centimetres on a plan represents 7 metres.
- At 1:1,000, a real length of 12 metres is 1.2 centimetres on a drawing.
- At 1:25,000, a real distance of 2 kilometres is 5 centimetres on a map.
A route is 7.5 centimetres long on a map with scale 1:60,000. What is the route's real length? Enter the number of kilometres.