Information about ratio

This article is about the mathematical concept. For the Swedish institute, see Ratio Institute.

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A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another.

Ratios are unitless when they relate quantities of the same dimension. When the two quantities being compared are of different types, the units are the first quantity "per" unit of the second — for example, a speed or velocity can be expressed in "miles per hour". If the second unit is a measure of time, we call this type of ratio a rate.

Fractions and percentages are both specific applications of ratios. Fractions relate the part (the numerator) to the whole (the denominator) while percentages indicate parts per 100.

A ratio can be written as two numbers separated by a colon (:) which is read as the word "to". For example, a ratio of 2:3 ("two to three") means that the whole is made up of 2 parts of one thing and 3 parts of another — thus, the whole contains five parts in all. To be specific, if a basket contains 2 apples and 3 oranges, then the ratio of apples to oranges is 2:3. If another 2 apples and 3 oranges are added to the basket, then it will contain 4 apples and 6 oranges, resulting in a ratio of 4:6, which is equivalent to a ratio of 2:3 (thus ratios reduce like regular fractions). In this case, 2/5 or 40% of the fruit are apples and 3/5 or 60% are oranges in the basket.

Note that in the previous example the proportion of apples in the basket is 2/5 ("two of five" fruits, "two out of five" fruits, "two fifths" of the fruits, or 40% of the fruits). Thus a proportion compares part to whole instead of part to part.

Throughout the physical sciences, ratios of physical quantities are treated as real numbers. For example, the ratio of $\text{[math]}$ metres to 1 metre (say, the ratio of the circumference of a certain circle to its radius) is the real number $\text{[math]}$ . That is, $\text{[math]}$ m/1m = $\text{[math]}$ . Accordingly, the classical definition of measurement is the estimation of a ratio between a quantity and a unit of the same kind of quantity. (See also the article on commensurability in mathematics.)

In algebra, two quantities having a constant ratio are in a special kind of linear relationship called proportionality.

Definitions and notation

Ratios are unitless when they relate quantities of the same dimension. When the two quantities being compared are of different types, the units are the first quantity "per" unit of the second — for example, a speed or velocity can be expressed in "miles per hour". If the second unit is a measure of time, we call this type of ratio a rate.

Fractions and percentages are both specific applications of ratios. Fractions relate the part (the numerator) to the whole (the denominator) while percentages indicate parts per 100.

A ratio can be written as two numbers separated by a colon (:) which is read as the word "to". For example, a ratio of 2:3 ("two to three") means that the whole is made up of 2 parts of one thing and 3 parts of another — thus, the whole contains five parts in all. To be specific, if a basket contains 2 apples and 3 oranges, then the ratio of apples to oranges is 2:3. If another 2 apples and 3 oranges are added to the basket, then it will contain 4 apples and 6 oranges, resulting in a ratio of 4:6, which is equivalent to a ratio of 2:3 (thus ratios reduce like regular fractions). In this case, 2/5 or 40% of the fruit are apples and 3/5 or 60% are oranges in the basket.

Note that in the previous example the proportion of apples in the basket is 2/5 ("two of five" fruits, "two out of five" fruits, "two fifths" of the fruits, or 40% of the fruits). Thus a proportion compares part to whole instead of part to part.

Throughout the physical sciences, ratios of physical quantities are treated as real numbers. For example, the ratio of $\text{[math]}$ metres to 1 metre (say, the ratio of the circumference of a certain circle to its radius) is the real number $\text{[math]}$ . That is, $\text{[math]}$ m/1m = $\text{[math]}$ . Accordingly, the classical definition of measurement is the estimation of a ratio between a quantity and a unit of the same kind of quantity. (See also the article on commensurability in mathematics.)

In algebra, two quantities having a constant ratio are in a special kind of linear relationship called proportionality.

More examples

The ratio of heights of the Eiffel Tower (300 m) and the Great Pyramid of Giza (139 m) is 300:139, so one structure is more than twice the height of the other (more precisely, 2.16 times).
The ratio of the mass of Jupiter to the mass of the Earth is approximately 318:1, meaning that Jupiter's mass in 318 times larger than the earth.
If two axles are connected by gear wheels, the number of times one axle turns for each turn of the other is known as the gear ratio, one familiar example of which is the number of turns of the pedals of a bicycle compared with number of turns of the rear wheel.
The ratio of hydrogen atoms to oxygen in water (H₂O) is 2:1, which means for every one oxygen atom, there would be two hydrogen atoms as well.
Most movie theater screens have an aspect ratio of 16:9, which means that the screen is 16/9 as wide as it is high.
In probability, the ratio of the probability of something happening to the probability of it not happening is called the odds of the thing happening.
In music, the interval of a perfect fifth is formed by two pitches, or frequencies, at a ratio of 3:2, with the higher note being 1.5 times the frequency of the lower.

External Links

Nicolaus Mercator's Ratio Theory at Convergence

Ratio is the research institute of the Swedish enterprise. The institute's infrastructure is financed by the Confederation of Swedish Enterprise, but the various research projects have financers like the Wallenberg foundation and the Swedish Free Enterprise Foundation.
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Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity.
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proportionality, see Proportionality (disambiguation).

In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.
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In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number.
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dimension (Latin, "measured out") is a parameter or measurement required to define the characteristics of an object—i.e., length, width, and height or size and shape.
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velocity is defined as the rate of change of position. It is a vector physical quantity, both speed and direction are required to define it. In the SI (metric) system, it is measured in meters per second (m/s). The scalar absolute value (magnitude) of velocity is speed.
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A rate is a special kind of ratio, indicating a relationship between two measurements with different units, such as miles to gallons or cents to pounds.

Example

When dealing with rates, the division operator is sometimes expressed as per.
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fraction (from the Latin fractus, broken) is a concept of a proportional relation between an object part and the object whole. Each fraction consists of a denominator (bottom) and a numerator (top), representing (respectively) the number of equal parts that an object is
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In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). It is often denoted using the percent sign, "%". For example, 45 % (read as "forty-five percent") is equal to 45 / 100, or 0.45.
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colon (“:”) is a punctuation mark, consisting of two equally sized dots centered on the same vertical line.

Punctuation

Usage

As with many other punctuation marks, the usage of colon varies among languages and, for a given language, among
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In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator an integer) is called "reducing a fraction".
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Physical science is an encompassing term for the branches of natural science, and science, that study non-living systems, in contrast to the biological sciences. However, the term "physical" creates an unintended, somewhat arbitrary distinction, since many branches of physical
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In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and
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1 metre =
SI units
1000 mm 0 cm
US customary / Imperial units
0 ft 0 in

The metre or meter^[1](symbol: m) is the fundamental unit of length in the International System of Units (SI).
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circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the centre.

Circles are simple closed curves which divide the plane into an interior and exterior.
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Measurement is the estimation of the magnitude of some attribute of an object, such as its length or weight, relative to a unit of measuremnt. Measurement usually involves using a measuring instrument, such as a ruler or scale, which is calibrated to compare the object to some
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commensurable iff a/b is a rational number.

The usage comes to us from translations of Euclid's Elements, in which two line segments a and b are called commensurable precisely if there is some third segment c
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Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Arabic^[1] mathematician, astronomer, astrologer and geographer,
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In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. This is in contrast to a variable, which is not fixed.

Unspecified constants

The most widely mentioned sort of constant
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prevew not available
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proportionality, see Proportionality (disambiguation).

colon (“:”) is a punctuation mark, consisting of two equally sized dots centered on the same vertical line.

Punctuation

Usage

As with many other punctuation marks, the usage of colon varies among languages and, for a given language, among
..... Click the link for more information.