![]() 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. non-terminating decimal numbers with infinitely repeating patternsĪny integer can be converted cleanly into a fraction, and is a rational number.įor example, 3 can be expressed as 3/1.There are four types of rational numbers: Though you learned what rational numbers are earlier in the article, it's helpful to break them up into broad categories, and look at different examples. And if a number can't be expressed this way, then it's an irrational number. ![]() So if a number can be expressed cleanly as a fraction, or a ratio between two integers, then it's a rational number. Some examples of rational numbers include:Īccording to Wikipedia, the term ratio "is derived from rational". Rational NumbersĪgain, a rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not 0: Source: Rational Numbers Integers are exactly like whole numbers, but can also include negative numbers. They do not include decimals or fractions, and since they start from 0 and go up, all whole numbers are positive. Note that whole numbers are just that – whole. Whole NumbersĪ whole number is any number from 0 up to infinity: 0, 1, 2, 3, 4, 5. What Are Whole Numbers and Integers?īefore getting into integers, it would be helpful to review what whole numbers are. In this article, we'll go over what whole numbers and integers are, cover different types of rational numbers, and learn how to determine if a number is rational or not. In other words, a rational number can be expressed as p/q, where p and q are both integers and q ≠ 0. A rational number is any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero.
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