Reading Scales

Look around and you will spot them everywhere: a ruler along the edge of your desk, the measuring jug in the kitchen, the weighing scale for the flour, the thermometer by the window, the speedometer on the dashboard of a car. Every one of them has a line of marks with numbers — a scale — and to use it you have to read it.

Here is the catch. The scale hardly ever numbers every mark. It numbers a few of them and leaves little unnumbered lines in between. The whole trick of reading a scale is working out one thing first: what is each little gap worth?

The method: count the gaps, then share out

You never have to guess. There is a sure-fire recipe that works on any scale — ruler, jug, dial or gauge:

Find two numbered marks next to each other.
Subtract to find the difference between their numbers.
Count the little gaps between those two numbered marks.
Divide the difference by the number of gaps — that is what one gap is worth.
Count on from a numbered mark, one gap at a time, to the pointer.

For example, between 0 and 10 with 5 equal gaps, each gap is 10 \div 5 = 2. So the marks read 0, 2, 4, 6, 8, 10. Once you know that, the rest is just counting.

the value of one division is \dfrac{\text{gap between numbered marks}}{\text{number of small intervals}};
read the pointer by counting divisions on from the nearest number;
if the pointer is between two marks, estimate how far along it sits.

Worked example 1 — a weighing scale

A kitchen scale is numbered 0 and 100 grams, with 5 equal gaps between them and no other numbers. What is each little gap worth?

The difference is 100 - 0 = 100, shared across 5 gaps: 100 \div 5 = 20. So the marks count up 0, 20, 40, 60, 80, 100 — each gap is 20 g, not 1 g! If the pointer sits 3 gaps past 0, that is 3 \times 20 = 60 grams.

Worked example 2 — a measuring jug

A measuring jug is marked 0 at the bottom and 1 litre at the top, with 10 equal gaps between. One litre is 1000 millilitres, so each gap is 1000 \div 10 = 100 ml.

Pour in some juice and it rises to the 4th mark. That is 4 \times 100 = 400 ml. Notice how badly it would go wrong to think each line meant "1" — you would read 4 ml instead of 400 ml, a hundred times too little!

Worked example 3 — reading a pointer

Here the numbered marks 0, 10, 20, 30 have small marks every 2 units (there are 5 gaps between each pair of numbers, and 10 \div 5 = 2). The pointer sits 2 small marks past 20, so it reads 20 + 2 + 2 = 24.

And what if the pointer stops between two marks? Then you estimate. Halfway between two marks each worth 2 is about one more, so a pointer resting halfway between 24 and 26 reads roughly 25.

The classic mistake is to assume every little line is worth 1. It very often isn't! You must always work out the gap value by counting the divisions between two numbered marks and dividing.

If 0 to 50 has 5 gaps, each gap is 50 \div 5 = 10 — not 1.
If 0 to 20 has 10 gaps, each gap is 2.
On the measuring jug above, each line was worth a whole 100 ml. Reading it as 1 would be 100 times wrong — enough to ruin a recipe or a science experiment.

So: count the gaps first, then read the pointer. Never assume.

This isn't just a school exercise. A nurse filling a syringe reads a tiny scale to give exactly the right dose of medicine — misread it and a patient could get far too much or too little. A pilot scanning the dials in a cockpit reads height, speed and fuel off scales in a fraction of a second. That is exactly why good instruments are designed with clear, well-spaced scales and bold numbers.

And here is the lovely part: the very same question — "what is each gap worth?" — unlocks any gauge or graph you will ever meet. A car's fuel gauge, a heart-rate monitor, a bar chart, a barometer: learn to read one scale and you can read them all.