Significant figures used to imply stated error? The question reads, " express each of the following quantities using significant figures to imply the stated error". 

a)$2.3 \pm 0.001$

b)$1.989 \pm 0.0003$

I think the first one is 2.300 because the zero in the thousands place implies an error of $\pm 0.001$ but how do I use sig figs to imply an error of $\pm 0.0003$?
The use of significant figures always implies some error, that is not explicitly stated. It is therefore irrelevant how big this error is. I merely states that the last digit is rounded. 

In the first case the quantity is given as $2.3\pm0.001$, which gives you the interval $(2.301;2.999)$, which is expressed as $2.300$ in significant figures.

The same applies to the second quantity, which is given as $1.989\pm0.0003$, which in turn gives you the interval $(1.9893;1.9887)$, which is expressed as $1.9890$.