Pull-down resistor calculator
A pull-down holds a floating input at ground. Its value trades leakage immunity against wasted current: 10 kΩ on a 3.3 V rail wastes 0.33 mA when the line is driven high, which is fine on mains power and significant on a coin cell.
How to choose a pull-down resistor
A pull-down is not simply an inverted pull-up, because most digital inputs are not symmetric. CMOS inputs leak only nanoamps, so a very high pull-down would technically work — until you account for board contamination, humidity and nearby switching noise coupling into a high-impedance node. Ten kilohms is the customary compromise: low enough to be immune to leakage and coupling, high enough that the current wasted when the line is driven high stays negligible. In a low-power design the calculation is worth doing properly, because a permanently-driven pull-down can easily outrun the sleep current of the microcontroller it is attached to.
Questions
10 kΩ suits most logic. Lower for noisy environments, higher only in careful low-power designs.