If you’re confused about whether negative numbers and decimal figures can be rational numbers, continue reading to demystify both types of numbers!

What is the key difference between rational numbers and their irrational counterparts?

Before you’re able to figure out whether a given number is a rational number or an irrational number, it’s important to be able to tell the key difference between both types of numbers.

Rational numbers are figures which can be easily written down as a whole fraction. Whereas their opposite, irrational numbers can’t be written down as a simple whole fraction.

You may be surprised to read that both decimal figures and negative figures can be classed as irrational numbers as well as rational numbers. Remember that if a negative number or a decimal number can be written down as a whole fraction, you’re dealing with a regular figure.

Are negative numbers rational?

As mentioned briefly above negative numbers can be rational or irrational, to figure out whether your negative number is rational, go ahead and try and turn your negative number into a whole fraction.

Another tip which you may want to use in order to tell if the number that you’re looking at is rational or irrational, check whether your negative number’s positive equivalent is a rational number. As if a negative number’s positive counterpart is negative, there’s a high likelihood that the number that the negative number that you’re trying to place is also an irrational number.

Is negative 1.5 a rational number?

If you want to have a go at classifying a negative number as a rational number or an irrational number, you may want to start off with an easy example, that is simple to sort such as -1.5. If you’re stuck, just make sure to try and write down -1.5 as a whole fraction. If you can successfully write down -1.5 as a whole fraction which has a whole numerator and a whole denominator, then -1.5 is a rational number. However, if you can’t turn -1.5 into a whole fraction, then -1.5 is an irrational number, not a rational number.

Examples of negative irrational numbers:

If you find it helpful to look at a list of examples of negative irrational numbers, in order to more easily be able to classify negative numbers, the following numbers are all negative irrational numbers, -2, -13 and -8.

Examples of decimal numbers that are irrational:

Just as negative numbers can be irrational, decimal numbers can be irrational too. One prime example that is great to keep in mind is the number pi. Pi is an infinite number, which doesn’t have reoccurring digits and which therefore is an irrational number. As there is no logical way that you can turn an infinite, endless number which has no end into a neat whole fraction.

Just be careful when you’re classing numbers not to automatically assume that decimals are always irrational as decimals which recurring numbers are almost always rational numbers.

If you’re ever confused about negative numbers or decimal numbers and whether they are rational or not, simply refer back to this handy article for answers.