Mehul's ruler is broken at the zero end, so it now starts at the 1 cm mark
Mehul's ruler is broken at the zero end, so it now starts at the 1 cm mark. He lines up one end of a pencil with the 1 cm mark, and the other end reaches 8.5 cm. Mehul says the pencil is 8.5 cm long. Jyoti says it is 7.5 cm long. Who has read it correctly?
Who do you think is right? Pick one.
The answer: Jyoti is right, the starting mark must be subtracted: 8.5 - 1 = 7.5
Why
Mehul is correct that a broken ruler can still be used — he doesn't need a new one. But a length is the distance between the two ends of the pencil, and his pencil doesn't start at zero; it starts at the 1 cm mark. Reading only the far end (8.5 cm) counts that first missing centimetre as part of the pencil, when it isn't. The correct way is to subtract the starting mark from the ending mark: 8.5 cm minus 1 cm gives 7.5 cm. In fact any clear mark can be the starting point — the 1 cm mark or even the 3 cm mark — as long as it is subtracted. Test: place the pencil so it starts at the 3 cm mark instead; the far end now reaches 10.5 cm, and 10.5 minus 3 is again 7.5 cm — the same length, as it must be. Jyoti is right: the pencil is 7.5 cm long, because the starting mark of 1 cm has to be subtracted from the reading of 8.5 cm.
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