The is an irrational number, because it cannot be expressed as a fraction a/b, where a and b are integers and b 0. In other words, this value can't be written as a fraction or as a repeating or terminating decimal. If we expressed it as a decimal, it would have an infinite number of digits to the right of the decimal point in a non-repeating pattern. The real-number system is made up of an infinite number of rational numbers (those that fit the fraction property above) and an infinite number of irrational numbers. There are many situations where a length is actually an irrational number (such as the hypotenuses of isosceles right triangles), so we cannot measure the length exactly. The idea that a measure is always an approximate value is a hard one to grasp, since in everyday life we treat measures as exact quantities.
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