Reading a Ruler

Start at the 0 mark

A ruler is a line of centimeters laid end to end, and the numbers count them from 0. To measure an object, put one end of it exactly on the 0 mark. Then read the number at the other end. That number is the length.

On many real rulers the 0 mark is a little way in from the end of the plastic. Line the object up with the 0 mark, not with the end of the ruler.

The object starts at the 2 mark, so its far end reads 8, but it is not 8 cm long. Slide it back until its left end sits on 0: the far end then reads 6, and the object is 6 cm long.

Count the spaces, not the marks

Each number on the ruler says how many centimeter spaces lie between it and 0. From 0 to 6 there are 6 spaces, each 1 cm long, so an object from 0 to 6 is 6 cm long.

The marks are not what you count. From 0 to 6 there are 7 marks, 0, 1, 2, 3, 4, 5 and 6, but only 6 spaces between them. A length is made of the spaces.

The object starts on 0 and ends on 6. It covers 6 spaces of 1 cm, so it is 6 cm long.

When the start is not 0

Sometimes the object does not start at 0, perhaps because the end of the ruler is broken. Here the object starts at the 2 mark and ends at the 7 mark.

The 7 at the far end counts the spaces from 0, but the first 2 of those spaces are not under the object. Take them off: 7 − 2 = 5. The object is 5 cm long. Count the spaces to check: from 2 to 3, 3 to 4, 4 to 5, 5 to 6 and 6 to 7 make 5 spaces.

So when an object starts part-way along, its length is the end reading take away the start reading.

The object runs from the 2 mark to the 7 mark: 7 − 2 = 5 cm.

Two ways to go wrong

Reading only the far end gives 7 cm. That would be right only if the object started at 0; here it starts at 2, so 2 cm come off.

Adding the two readings gives 7 + 2 = 9 cm, which is longer than the whole stretch of ruler from 0 to 7. The length is the gap between the two readings, so subtract.