What makes a number irrational or rational

Calculus Gifs. How to make an ellipse. Volume of a cone. Best Math Jokes. Our Most Popular Animated Gifs. Math Riddles. Is rational because you can simplify the square root to 3 which is the quotient of the integer 3 and 1. All repeating decimals are rational. Kiger Mar 25, When you hear the words "rational" and "irrational," it might bring to mind the difference between, say, the cool, relentlessly analytical Mr. Spock and the hardheaded, emotionally volatile Dr.

Unless you're a mathematician , though, you probably don't think of ratios between integers versus square roots, the sort of stuff that makes the non-mathematicians among us feel as confused as we do hearing Queen's "Bohemian Rhapsody" sung in Klingon. But in the realm of mathematics, where words sometimes have specific meanings that are very different from everyday usage, the difference between rational and irrational numbers doesn't have anything to do with reasoning and logic versus raw emotional urges.

He's a professor in the department of mathematics and statistics at Boston University and the director of the university's Rafik B. You can express either a whole number or a fraction — parts of whole numbers — as a ratio, with an integer called a numerator on top of another integer called a denominator.

You divide the denominator into the numerator. Irrational numbers, in contrast to rational numbers, are pretty complicated. As Wolfram MathWorld explains, they can't be expressed by fractions, and when you try to write them as a number with a decimal point , the digits just keep going on and on, without ever stopping or repeating a pattern.

So what sort of numbers behave in such a crazy fashion? Basically, ones that describe complicated things. Irrational numbers can be represented in the decimal form but not in fractions which implies that the irrational numbers cannot be expressed as the ratio of two integers. Solved Examples. Solution: 16 is a perfect square i.

As we know the square root of prime numbers are irrational numbers. Quiz Time. Which of the Following Numbers is Irrational?

Is the Square Root of Rational number. Irrational number. Which of the Following Numbers is Rational? So we can tell if it is Rational or Irrational by trying to write the number as a simple fraction. The answer is the square root of 2 , which is 1. Pi is a famous irrational number. People have calculated Pi to over a quadrillion decimal places and still there is no pattern.

The first few digits look like this:. The number e Euler's Number is another famous irrational number.