Reading Between the Marks on an Axis

Before reading any scale, work out what one small gap is worth: take two labelled marks, subtract, and divide by the number of gaps between them. From nought to twenty with four gaps, each gap is five. Then the arrow sitting two gaps above twenty reads thirty. The one trap is counting marks instead of gaps — five marks have only four gaps between them.

Count from whichever labelled mark is nearer, because fewer steps means fewer mistakes. With labels every twenty and gaps of five, an arrow three gaps above forty reads fifty-five — and counting down instead, one gap below sixty gives sixty take five, fifty-five again. Those two routes have to agree, and if they do not, you miscounted the gaps. That disagreement is the built-in check.

A pointer sitting halfway between two marks reads half of one gap more than the lower mark — half a gap, not half a unit. With gaps of ten, halfway past forty is forty-five, not forty point five and not forty-one. With gaps of two it would be one, and with gaps of fifty it would be twenty-five. Work out the gap first and this question answers itself.

The method does not change with the instrument. A jug, a dial, a thermometer, a ruler and a graph axis all want the same three moves: find two labels, count the gaps between them and divide to get one gap, then count from the nearest label. The jug here is labelled every hundred millilitres with a mark every fifty, so a level one mark above three hundred reads three hundred and fifty.

Three moves, in order: work out the gap value, count from the nearest label, then check by counting from the other side. Guessing a reading from how far up the scale it looks is what these questions are designed to punish, because two scales that look identical can have gaps of two and gaps of fifty. Quiz and exercises now.