4. The mass of a silver liberty (coin) was measured three times and each measurement was made to five digits. The mass values were 12.519 9.12.521 g, and 12.496 g. The average mass was
reported as 12.512 g.
Why is the average mass of the gold coin reported to five significant figures, even though you
had to divide by "3" to obtain the average?

The average mass of the gold coin reported to five significant figures, even though you  had to divide by "3" to obtain the average.

Explanation:

Given that,

The mass of a silver liberty was measured three times and each measurement was made  to five digits.

The mass values are,

The average mass of the gold  coin is 12.512 g.

We know that,

Significant figures :

Significant figures is explained the nonzero, leading zero and zeros between two nonzero digits.

For example,

The digits is 0.003405

In the digit, 345 = nonzero

0.00 = leading zero

The average mass of the gold coin reported to five significant figures because average mass is 12,512. All digits are nonzero.

Nonzero digit are significant.

Hence, The average mass of the gold coin reported to five significant figures, even though you  had to divide by "3" to obtain the average.