Final answer:
Dimensionless quantities do not have units and are used to compare ratios. Dimensionally correct equations have consistent units on both sides. Changing the system of units does not change the numerical value. The dimension of a physical quantity can be a fraction.
Step-by-step explanation:
Dimensionless quantities are quantities that do not have units. They are used to compare the ratios or proportions of different physical quantities. For example, the angle in radians is a dimensionless quantity as it represents the ratio of the arc length to the radius of a circle.
A dimensionally correct equation means that the units on both sides of the equation are the same. This ensures that the equation is consistent with the dimensions of the physical quantities involved. For example, in the equation F = ma, the dimension of force (F) is the same as the dimension of mass (m) multiplied by the dimension of acceleration (a).
A change in the system of units does not change the numerical value of a physical quantity. However, it may change the representation of the quantity in terms of different units. For example, if a temperature of 25 degrees Celsius is converted to Fahrenheit, the numerical value will change, but the physical quantity remains the same.
The dimension of a physical quantity can be a fraction. Dimension refers to the fundamental properties of a physical quantity, such as length, time, mass, etc. These properties can be combined in different ways, including fractions, to form the dimensions of other physical quantities. For example, velocity is defined as the ratio of distance (length) to time, which gives it the dimension of length divided by time.
Learn more about Dimensionless quantities and dimensional analysis