Q1.
Oh, the number of handspans is different for all of us. So, what can we say about the length of the table?
Answer
Very little that is useful! All we can honestly say is that the table is about 13 to 14 handspans long — and even that sentence is incomplete, because it does not say whose handspan.
| Name of the student | Number of handspans |
|---|---|
| Anish | Slightly more than 13 |
| Padma | 13 |
| Tasneem | Slightly less than 13 |
| Deepa | Between 13 and 14 |
| Hardeep | 14 |
The length of the table never changed while the five friends measured it. Only the unit changed — and so the number changed.
Length of table = number × size of one handspan
The length is fixed, so a bigger handspan gives a smaller number,
and a smaller handspan gives a bigger number.
The length is fixed, so a bigger handspan gives a smaller number,
and a smaller handspan gives a bigger number.
A measurement is only meaningful if the person hearing it can reproduce it. “13 handspans” cannot be reproduced by anyone else, so it is not a proper measurement of the table. We need a unit that is the same for everybody.
Why it happens: a length is expressed in two parts — a number and a unit. If the unit is not fixed, the number carries no information. Saying “the table is 13 long” is as vague as saying “the bag costs 50” without saying rupees.