Identify a rational number by checking to see if it can be represented as p/q, where q≠0. Then, ensure you can further simplify the p/q ratio and translate it into decimal form. For example, ¾ is a rational number because it can be calculated as a fraction where q (4) does not equal 0, and its decimal form (. 75) is finite.

Identifying an irrational number is simple! Check to see if it can be expressed as a fraction, where p and q are integers and q ≠ 0. If it can’t, then it’s an irrational number. For example, √2 (the square root of 2) is irrational. When expressed as a decimal, it becomes the number 1. 41421356237…, which cannot be made into a simple fraction.

A decimal number does not need both properties to be rational; it can be either finite or recurring. An example of a finite decimal would be . 875, which can be expressed as the rational number ⅞. An infinite but recurring decimal like 9. 45454545… is rational. You can identify it by looking at the numbers after the decimal point; the “45” repeating pattern confirms this number as rational.

These numbers are rational because they can all be expressed as a simple fraction, p/q, where q ≠ 0. For example, 2 becomes 2/1, -2 becomes -2/1, and so on. Since a rational number is defined as a ratio or fraction made from 2 integers, any integer, whole, or natural number qualifies as rational.

For example, √49 is a rational number. When you solve to find the square root of 49, the answer is 7 (an integer expressed as the square of 49, another integer), which can also be written as the fraction 7/1.

⅚ and ⅙ are both rational numbers because they are simple fractions made from whole numbers.

√5 is irrational. When you solve for the square root of 5, the result is 2. 2360679775…, which can’t be converted into a simple fraction.

A number like 3. 605551275… is irrational. If you look at it, you can see that it’s both non-terminating (indicated by the ellipses) and non-repeating (the numbers do not make a pattern).

For example, √2 is a surd. When solved, √2 is 1. 41421356237…, which isn’t a whole number and can’t be expressed as a fraction.

√2 is irrational. When you multiply the square roots √2 and √3, the answer is √6, which is also irrational. When you multiply √2 and √2, the answer is √4—which is a perfect square and a rational number.

Note that the denominator of a rational number can be any real number at all, so long as it isn’t 0.