Is 0 closer to 0.003 than 0.01?

The smaller the value the closer it is to zero.

.003 < .01, therefore .003 is closer to zero.

On a number line (not to scale):

---(0)--(.001)-(.002)-(.003)-(.004)-(.005)-(.006)-(.007)-(.008)-(.009)-(.010)-(.011)

Notice how .003 is closer to 0 than .010