1. Determine the Charge Transfer:

* The plastic rod initially has a charge of -3 nC.

* After touching the sphere, the rod has a charge of -10 nC.

* This means the rod lost a charge of -10 nC - (-3 nC) = -7 nC.

* Since the rod lost negative charge, it means electrons were transferred to the sphere.

2. Calculate the Number of Electrons:

* The charge of a single electron is approximately -1.602 x 10⁻¹⁹ Coulombs (C).

* We need to convert the charge transfer from nanocoulombs (nC) to Coulombs: -7 nC = -7 x 10⁻⁹ C.

* Divide the total charge transfer by the charge of a single electron to find the number of electrons:

(-7 x 10⁻⁹ C) / (-1.602 x 10⁻¹⁹ C/electron) ≈ 4.37 x 10¹⁰ electrons

Answer: Approximately 4.37 x 10¹⁰ electrons were transferred from the plastic rod to the metal sphere.