There are no units because it is simply a ratio
There are many different ways to write 5m in metric units: .005 km .05 hm .5 dam 50 dm 500 cm 5000 mm
A meter stick is marked in centimeters and meters, which are units of the metric system, while a yardstick is marked in inches and yards, which are units of the imperial system. The length of a meter stick is designed to be 1 meter to easily measure objects in metric units.
Two measurements are equal when they have the same numerical value, for example 1 inch is equal to 2.54 centimeters. To show equality between measurements, they must have the same units, or be converted to the same units for comparison.
Joules and Fahrenheit are two different units that measure different quantities - energy and temperature, respectively. They cannot be directly converted to each other because they are not the same type of measurement.
Rate
Time
rate
For two measurements to be a conversion factor, they must represent the same quantity but in different units. The ratio should equal 1 and can be written as a fraction where the units cancel out, allowing you to convert from one unit to another.
If you have two items using different units of measurement, you must first convert to the same type in to percentage. Then, you can compare the ratio, It is called coefficient of variability. For example if you want to compare length with weight of two variables or populations, then first convert the measurements in percentage and then go for comparision.
If the two measurements are of the same type, such as length, we could use that ratio to convert from one measurements to another. An example is the ratio of 1.609 Km to 1 mile. Here, we can multiply some number of miles by 1.609 and find the kilometer distance. If the two measurements are of different types, that is often used as a definition of another quantity such as speed. Speed is defined as the ratio of the distance traveled to the amount of time it takes. These two examples are the most common uses when taking the ratio of two measurements, yet there may be a more generalized term or theorem here, but I've not heard of it yet.
There is no real reason for two equivalent measurements to be rationed! The ratio of two equivalent measurements will depend on the units used. The ratio between a length in feet and the equivalent length in inches, for example, is 12:1.
conversion factor
They are different because a ratiocompares two different numbers or measurements from different units but the rate does not. They are similar because they both compare numbers. EX) ratio: 4/3 rate: 1.333 etc.
what is it
In a ratio of measurements for the same kinds of units, units get canceled. For example, in a ratio of 3 meters / 8 meters, you can cancel the "meters" in the numerator and the denominator. An important ratio is pi, which is the ratio of the circumference of a circle to its diameter. If you measure the circumference in feet, and the diameter in feet, then divide circumference/diameter, then the result is the dimensionless quantity 3.14159265.... If you go back and measure both in meters, you get the same answer.In a ratio of two measurements, the units cancel, so it makes no difference whether you write the units, or not.
A rate.