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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