A concrete number or ''numerus numeratus'' is a
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
associated with the things being counted, in contrast to an abstract number or ''numerus numerans'' which is a number as a single entity. For example, "five apples" and "half of a pie" are concrete numbers, while "five" and "one half" are abstract numbers. In mathematics the term "number" is usually taken to mean an abstract number. A denominate number is a type of concrete number with a
unit of measure
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multi ...
attached with it. For example, "5 inches" is a denominate number because it has the unit ''
inches
Measuring tape with inches
The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelfth") ...
'' after it.
History
Mathematicians in ancient Greece were primarily interested in abstract numbers, while writers of instructional books for practical use were not concerned with such distinctions, so the terminology distinguishing the two types of number was slow to appear. In the 16th century textbooks began to make the distinction. This has appeared with increasing frequency until modern times.
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Denominate numbers
Denominate numbers are further classified as either simple, meaning a single unit is given, or compound, meaning multiple units are given. For example, 6
kg is a simple denominate number, while 324
yards
The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. Since 1959 it has been by international agreement standardized as exactly ...
1
foot 8
inches is a compound denominate number. The process of converting a denominate number to an equivalent form that uses a different unit is called reduction. More specifically, reduction to a lower or higher unit of measurement is called reduction to lower or higher denominations. Reduction to a lower denomination is accomplished by multiplying by the number of lower units contained in each higher unit. In the case of a compound denominant number, the products are then added together. For example, 1 hour 23 minutes 20 seconds is 1 h × 3600 s/h + 23 min × 60 s/min + 20 s = 5000 seconds. Similarly, a division is used to reduce to a higher denomination, and remainders can be applied to the next highest unit to form compound denominant numbers. Addition and subtraction of compound numbers can be performed by grouping the amounts associated with each unit and performing the necessary
carry and borrow operations. Multiplication and division by a pure number are again similar.
See also
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Dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as mi ...
*
Units of measurement
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multi ...
References
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Numbers
Measurement