Lesson 2 of 6

Reading a scale.

About 25 minutes · 6 practice questions

Every measuring instrument reads to its smallest division: reading to the nearest mark, the uncertainty of a reading, measuring from a mark other than zero, and how to write the result down.

Step 1 of 6 · To the nearest mark

Step 1 of 6

To the nearest mark

The board has a ruler with a bar on it. The ruler is marked only in whole centimetres: its smallest division is 1 cm. The end of the bar falls between two marks, and what lies between them the ruler cannot say. So you read the mark nearest the end.

Answer, then choose Read under Look inside to check: the reading appears under the ruler.

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Step 2 of 6

The uncertainty

The end of the bar is closer to the mark for $3$ ⁠ than to any other mark. So how far from it can it be? No more than halfway to the next mark, either side. That distance is the uncertainty of the reading: how far the true end can be from the number you read. It is written with $\pm$ ⁠ after the number.

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Step 3 of 6

Closer marks

The uncertainty comes not from the bar but from the ruler: it is half the ruler’s smallest division. Predict what will happen when the ruler is swapped, then look at the bottom line on the board.

Try it: after predicting, slide Smallest division between 1 cm, 0.5 cm and 0.1 cm, and watch the reading and the uncertainty.

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Step 4 of 6

Reading millimetres

On this ruler each centimetre is split into ten millimetres, and the half-centimetre mark is a little longer so they are easy to count. First read the whole centimetres before the end, then count millimetres up to the mark nearest the end. The dashed line drops from the end onto the marks.

You can zoom in on the board to count. Answer, then choose Read under Look inside.

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Step 5 of 6

Measuring from a mark other than zero

Sometimes the end of a ruler is worn, and you measure from the 1 cm mark instead. Then you read two ends: where the bar starts and where it stops. The length is the difference between them. Each of the two readings can be half a division off the true end, so the uncertainty of the length grows to a whole division.

Answer, then choose Read under Look inside: the two dots on the ruler mark the two readings.

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Step 6 of 6

Writing it down

The result of a measurement has three parts: the number, the unit and the uncertainty. In the number, write every digit the ruler really read, and no more: a digit the ruler cannot read is a guess, even if a calculator prints it.

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Interactive scene

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Each step sets up the Scene for you, and a control marked “fixed” stays put for that step.

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