Acceleration due to Earth’s gravity is \(-9.8 m/s^2\). Which part of this number gives the information on direction, making it a vector quantity?

Vector quantities carry meaning of direction and magnitude.
\(F=9 \times 10^9N \times m^2c^2 \frac{\mathrm{45 \times 10^{-6} \times 30 \times 10^{-6}} }{\mathrm{(0.60)^2}} = 33.75N\)
Scalar quantities only carry meaning in regards to the magnitude of the quantity.
The gravitational acceleration constant for Earth: \(-9.8 m/s^2\) is the unit of the quantity. This tells us that the quantity is acceleration (because the units of acceleration are length/time2). It also tells us that we are working in SI units. If a problem gives quantities in another metric system, we must convert something.
9.8 is the magnitude of the quantity. This tells us how much of the quantity we have. We can find this, if the problem asks for it, by taking the absolute value of the quantity
– (The negative sign) gives us the direction of the quantity. In cases where the value is positive, the positive sign + is usually omitted. We know that the quantity is a vector based on context and its name. For example, a car’s speedometer tells you the speed of the car is 35mph. We know that speed is a scalar quantity and so we cannot say anything about its direction. If a problem tells you that a ball is thrown with a velocity of 35 mph, you can assume the ball is not being thrown backward and this sets your frame of reference for the rest of the problem.
Gravity on Earth pulls us to the surface. So we know that the negative sign on the gravitational acceleration constant tells us that gravity is downward.