How to Use a Venn Diagram to Classify Rational Numbers?

A Step-by-step Guide to Using a Venn Diagram to Classify Rational Numbers

Using a Diagram to Classify Rational Numbers – Examples 1

Using a Diagram to Classify Rational Numbers – Examples 2

Solution:

Step 1: Draw a large rectangle to represent the set of all real numbers.

Step 2: Draw two overlapping circles inside the rectangle, one to represent the set of rational numbers and the other to represent the set of irrational numbers.

Step 3: Label the circle representing rational numbers as \(“Q”\) and the circle representing irrational numbers as \(“I”\).

Step 4: Shade the region inside the circle \(“Q”\) to show all the rational numbers. This includes all fractions, integers, terminating decimals, and repeating decimals.

Step 5: Shade the region inside the circle \(“I”\) to show all the irrational numbers. These include numbers that cannot be expressed as a ratio of two integers, such as the square root of \(2\) or pi.

Now we can classify the given numbers:

\(-4\): Rational (an integer)

\(\frac{7}{9}: Rational (a fraction)

\(\sqrt{9}\): Rational (an integer)

\(0.75\): Rational (a terminating decimal)

\(\sqrt{5}\): Irrational (a number that cannot be expressed as a ratio of two integers)

\(2.4\): Rational (a terminating decimal)

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