Accurate to N decimal places does not necessarily mean N digits have to be same; it actually means that the result must be within half of the (N+1)th digit... i.e. you have to round the Nth digit using the (N+1)th digit.
e.g. PI (3.14159265...) to 3 decimal places is 3.142 and not 3.141. The first has an error of ~-4E-4, and the second ~5.9E-4. The second value is less correct than the first, and has an error of more than half the (N+1)th digit i.e. ~5E-4.
The accuracy within X means that the value you present must be within X of the actual result. As you can see in the above examples, the values are out by ~4E-4 and ~5.9E-4 respectively. If asked for PI within 0.0001, we could write 3.1416 which has an error ~7.3E-6, which is obviously less than (i.e. within) 0.0001.