When is a zero not significant?

Not between significant digits.

Explanation:

A zero not significant when it's not between significant digits.

Zero are not significant when indicating the decimal point position

Explanation:

The number zero has a special meaning with respect to its meaning, when it is placed to the right as a decimal, its meanings so precision measurements were made, for example 10 cm and 10.0 cm, the first one has an accuracy of one centimeter and the second has an accuracy of 0.1 cm.

In the case of being placed to the left of all numbers, the meaning is to indicate where the decimal point goes, but it does not give information about the accuracy of the measurement, in this second case the zeros are not significant, for example: 0.1 0.0001 in these two cases are not significant