The term gross means a few different things, depending on the context. As a unit of measurement, a gross is equal to 12 dozen (12 × 12), or 144.
Gross is also used as a modifier to describe some total quantity before any deductions, such as the amount of sales, salary, and profit. For example, if Sally sells 30 cookies at her school bake sale for $1.50 each, her gross sales can be calculated by multiplying the sale price by the number of cookies sold:
30 × 1.50 = 45
Sally's gross sales were therefore $45. This number doesn't take into account how much money (or time) Sally spent to make and sell the cookies. Similarly, a person's gross salary is how much they earned before deductions such as taxes.
Gross as a unit of measurement
A gross, also referred to as a "dozen dozen" or a "square dozen" is just one measure based on the dozen. There is also a measure called a small gross (ten dozen), as well as a great gross (twelve gross). The table below shows their measures.
|Small gross||120 (12 × 10)|
|Great gross||1728 (123)|
The above measures are based on the duodecimal system. The duodecimal system, like the decimal numeral system (the most widely used system in the world), is a positional numeral system. The two systems differ in terms of the base used; the base of the duodecimal system is 12, while the base of the decimal numeral system is 10.
In a positional numeral system, each position represents a power of the base. The base in the decimal numeral system is 10, and the base in the duodecimal system is 12. The numeral "10" in the decimal system is the number ten. The same numeral 10 in the duodecimal system, converted to the decimal system, is 12. This is because of the different base used. For comparison, below are the expansions of the numeral "10" in both the decimal and duodecimal system:
10 = 1 × 101 + 0 × 100 = 10 + 0 = 10
10 = 1 × 121 + 0 × 120 = 12 + 0 = 12
Did you know?
School pencils are often ordered by the gross. There are 12 pencils in each package, and 12 packages in each gross of pencils.