If you’ve been reading up on irrational numbers to try and understand the differences between irrational numbers and rational numbers, simply continue reading to discover a handy guide to both irrational numbers and rational numbers.

What is a rational number?

A rational number is any number which can be written down as a whole fraction. If you’re wondering what a whole fraction is, a whole fraction features two full numbers and does not feature any numbers which have decimal points.

Remember that fractions feature two numbers, a numerator and a denominator, when a rational number is described as being rational both numbers, the numerator and the denominator must be full numbers.

What is an irrational number?

Unlike a rational number, irrational numbers can’t be described using whole fractions. Many numbers which feature decimal points are irrational numbers. An obvious example being pi, which is 3.14159265359 and which can’t be expressed as a fraction with whole numbers.

However, if you assumed that all decimal figures are classed as being irrational, think again. There are examples, where numbers which feature decimal points can actually be expressed as whole fractions. So be sure to think twice before you assume that a number is an irrational number.

Can irrational numbers be negative?

If you were curious about whether or not an irrational number could be negative, the answer is yes, negative numbers can be negative or positive, just like any other number. Furthermore most negative versions of normal irrational numbers also happen to be irrational.

Is the number zero a rational or irrational number?

The number zero is a rational number as zero can be divided by itself to give a full number, zero. So if a friend tries to tell you that zero is an irrational number, make sure to teach them that zero is in fact a rational figure.

Are there any other methods that can help you find rational numbers?

Yes, if you notice then a number has recurring digits after its decimal point, the number which you’re looking at is in fact a rational number.

Rational numbers are also the numbers which you’re far more likely to use on a daily basis, such as full numbers like 1,2,3,4,5,6,7,8,9 and 10. As all full numbers happen to be rational numbers. A fact that is useful to try to remember.

Why is it necessary to know about both rational numbers and irrational numbers?

Even if you are now clear about what constitutes a rational number and what constitutes an irrational number, you may be wondering what the point of being able to tell the two apart is.

The simple answer is that to perform some complicated mathematical calculations, you’ll need to use different methods and formulas, depending on whether the number that you’re dealing with is a rational number or an irrational number.

So if you see yourself dealing with algebraic formulas in the future, it’s definitely essential to be able to identify both types of numbers. So that you’ll be able to use the right formula or equation.

Irrational numbers can be tricky, but understanding their properties—including whether they can be negative—opens the door to deeper mathematical insight. While exploring irrational numbers, it’s important to remember that rational numbers can be negative.

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