# Rational & Irrational Numbers Worksheets

What is the Difference Between Rational & Irrational Numbers? It's all about the numbers in mathematics, isn’t it? It is nothing without a number game. But what exactly is a number? A number is an arithmetic value which can be a figure, word or symbol indicating a quantity. There are infinite types in numbers; natural, whole, integers, real, and complex numbers. One of the types which is the real numbers type is further divided into rational and irrational number. In most problems, you will find rational and irrational very commonly. A set of Rational numbers involve having integers and fraction; on the other hand, irrational numbers are numbers that cannot be expressed as fractions. : In mathematics, a rational number is any number that you can represent it in the fractional form like p/q, where q is greater than zero(0). You can use rational numbers as a fraction. But you will write their denominator & numerator as integers, and denominator will be equal to zero(0). Key points about rational numbers: While solving rational numbers (Q), the following points must be in your mind: Real numbers (R) contain all ration numbers (Q) and integers (Z). We can write integers as natural numbers (N). We can express all rational numbers as a whole number because we can write them in a fractional form. How to verify rational numbers: If you want to identify a given number is rational or not, don't forget to check these considerations: The number must be in fraction form like p/q, where q≠0. You can further simplify ratio p/q and express it in decimal form. The set of rational numbers must have +ve & -ve numbers and zero. Example: Verify 1 1/2 is a rational number. Solution: By simplifying, 1 1/2 becomes 3/2. Numerator 3 is an integer. Denominator 2 is an integer that is 2 ≠ 0. Hence proved 3/2 is a rational number. The difference between the two are: 1. Rational numbers can be expressed in a ratio of two integers, while irrational numbers cannot be written or expressed in a ratio of two integers. 2. Rational numbers can be expressed in a fraction; irrational numbers cannot be expressed in fractions. 3. Most of the rational numbers are perfect squares while no irrational number is a perfect square. 4. Rational numbers are finite or recurring decimals, whereas irrational numbers are not.

• ### Basic Lesson

Demonstrates general rules of Rational & Irrational Numbers. Is -72 a rational or irrational number? The number is terminating and can be represented on number line, This indicates that it is a rational number.

• ### Intermediate Lesson

Explores how to approach complex Rational & Irrational Numbers. Is 0.784543189... a rational or irrational number? As this number is not terminating, it goes on and on and on… This is an irrational number.

• ### Independent Practice 1

Determine whether these numbers are rational or irrational. The answers can be found below.

• ### Independent Practice 2

Features another 20 Rational & Irrational Numbers problems.

• ### Homework Worksheet

Rational & Irrational Numbers problems for students to work on at home. Example problems are provided and explained.

• ### Topic Quiz

10 Rational & Irrational Numbers problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### The Most Prolific Mathematical Writer?

Who was the most prolific mathematical writer of all time? Hint: He made large bounds forward in the study of modern analytic geometry? Answer: Leonhard Euler. We owe Euler for the notation f (x) for a function (1734), e for the base of natural logs (1727), I for the square root of -1 (1777), p for pi, for summation (1755), the notation for finite differences y and 2y and many others.