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.
No. If it is a ratio (as it is) then it has no units: it is a pure number.
It is simply the first measurement divided by the second, expressed with their measurement units as a ratio.
Directions are expressed as units of
The ratio of 31 to 13 can be expressed as 31:13. To simplify, you can divide both numbers by their greatest common divisor, which is 1 in this case, so the ratio remains 31:13. This indicates that for every 31 units of one quantity, there are 13 units of another.
scale drawing
No. If it is a ratio (as it is) then it has no units: it is a pure number.
In economics, the units of measurement for elasticity are typically expressed as a ratio or percentage, without specific units. It is a measure of how responsive one economic variable is to changes in another variable.
scale drawing An example might be 4:1 This is a ratio in its simplest form (it cannot be further simplified mathematically) and it's expressed with no units (not in inches or milimeters etc).
Means for every 100 units of one, you add 12 units of 2. Or a 20/3 ratio (expressed in percent).
It is simply the first measurement divided by the second, expressed with their measurement units as a ratio.
Units
No, it is a ratio - without units.
Directions are expressed as units of
Coefficients of friction are unitless values because they represent the ratio between the force necessary to overcome friction and the force pressing two surfaces together. Since the units cancel out in this ratio, coefficients of friction are expressed as pure numbers without units.
The ratio of 31 to 13 can be expressed as 31:13. To simplify, you can divide both numbers by their greatest common divisor, which is 1 in this case, so the ratio remains 31:13. This indicates that for every 31 units of one quantity, there are 13 units of another.
Efficiency is typically expressed as a percentage, representing the ratio of useful output to input. It can also be expressed as a dimensionless ratio or a specific unit depending on the context, such as miles per gallon for fuel efficiency or lumens per watt for electrical efficiency.
The surface area of a shape is expressed in square units.