The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is the difference in the masses of the pieces to correct significant figures ?

To find the difference in the masses of the two gold pieces to the correct number of significant figures, we follow these steps:

Given data:
Mass of the first gold piece, $m_1=20.17\text{g}$
Mass of the second gold piece, $m_2=20.15\text{g}$

Step 1: Calculate the difference in mass.
$\text{Difference}=m_1-m_2$
$\text{Difference}=20.17\text{g}-20.15\text{g}=0.02\text{g}$

Step 2: Apply the rules of significant figures for subtraction.
When subtracting numbers, the final result should be rounded to the same number of decimal places as the measurement with the least number of decimal places.
Both $20.17\text{g}$ and $20.15\text{g}$ have 2 decimal places.
Therefore, the result must also have 2 decimal places.
Our calculated difference is $0.02\text{g}$, which already contains exactly 2 decimal places.

Thus, the difference in the masses of the pieces to the correct significant figures is 0.02 g.