Some meters show a left-justified '1' when the input is over-range. So a 1bb.b (where the 'b' represent spaces) means that the resistance exceeds 199.9 ohms.
A reading of bb1.0, on the other hand, means that the resistance is measured to be 1.0 ohm.
Normally on a low resistance scale the meter may not read exactly zero because of the resistance of the leads. If you take the reading with the leads shorted and subtract that from the reading you get on the test device you'll likely have a more accurate idea of what the resistance is.
Anyway, continuity beep threshold in a multimeter would normally be something like 100 ohms (so a 500W/120V heater would result in a beep but a 10W/120V heater would not). For example, the EX410 has a 150\$\Omega\$ threshold.
So just look at the reading and decide if it looks more like a short or more like a resistance, based on the resistances in your circuit. I would normally consider something that's in the 1\$\Omega\$ range a short unless there are really long or thin wires involved.