An irrational number cannot be written as just a ratio, such as p/q, where p and q are positive integers and q is greater than zero. If you found this article on rational numbers helpful, consider sharing it so more people can benefit from it.Īlso, feel free to reach out on Twitter and let me know what you think.Irrational numbers are those that cannot be expressed as fractions. And as computing power increases, so will that record.īut as far as anyone can tell, within those endless digits there are no repeating patterns, so pi is considered an irrational number. At the time of writing, the world record for the number of digits of pi that have been calculated is 62.8 trillion. But they don't contain infinitely repeating patterns, so they're considered irrational.įor example, while pi is often shortened to 3.14159, that's just an approximation. Numbers like pi (π = 3.1415926536.) and many square roots (√2 = 1.41421356237.) have digits that go past the decimal point infinitely. Irrational NumbersĪny number that does not meet the definition of a rational number is an irrational number. These types of numbers are not rational numbers, and are known as irrational numbers. However, there are decimal numbers that go on infinitely that do not contain repeating patterns. This means that the number can be converted into the fraction 1/3, and is a rational number.īut what about a more complicated number, like 0.142857142857.? Again, the 142857 pattern after the decimal repeats infinitely, and the number can be converted to 1/7, which is rational. Even though this is often simplified as 0.33, the pattern of 3's after the decimal point repeat infinitely. But this is a bit tricky, because the pattern must repeat infinitely.įor example, take the number 0.33333. Non-terminating Decimal Numbers With Infinitely Repeating Patternsĭecimal numbers that go on forever with repeating patterns are rational numbers. For instance, 0.0001 can be expressed as 1/10,000, meaning that it's a rational number.Īs long as a decimal number eventually terminates, without rounding or approximation, it's a rational number. This can be converted to 1/2, which means its a rational number.Įven longer terminating decimal numbers can be cleanly converted into fractions. Terminating Decimal NumbersĪny decimal number that terminates, or ends at some point, is a rational number.įor example, take the decimal number 0.5. Fractions Made up of IntegersĪny fraction made up of integers is a rational number, as long as the denominator is not 0.įor example, 1/3, -5/3, and 27/-463 are all rational numbers. For example, 0/1, 0/-4, and 0/18,572 are all valid fractions, and meet the definition of a rational number. The number 0 is also a rational number, because it can be converted into a fraction. This works for negative integers like -2 (or -2/1) and -2006 (or -2006/1). And since both the numerator (3) and denominator (1) are integers, and the denominator is not 0, then 3 is a rational number.
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