Classify each number as either rational or irrational. Drag and drop into its correct category.

Question

Rational
Irrational
Drag & Drop the answer
3.8‾3.\overline{8}3.
8


π\piπ
−117-\frac{11}{7}−
7
11
​


81\sqrt{81}
81
​


2\sqrt{2}
2
​

Answer 1

Let's classify each number:

1. Rational - A rational number can be expressed as the quotient of two integers.

   • \( 3.\overline{8} \) (which can be expressed as \( \frac{38}{9} \))
   • \( -\frac{11}{7} \)
   • \( \sqrt{81} = 9 \) (since 9 is an integer)

2. Irrational - An irrational number cannot be expressed as a simple fraction.

   • \( \pi \) (a well-known irrational number)
   • \( 2\sqrt{2} \) (since \( \sqrt{2} \) is irrational, and multiplying an irrational number by a non-zero rational number is irrational)

Now, here's the classification:

Rational:

• \( 3.\overline{8} \)
• \( -\frac{11}{7} \)
• \( \sqrt{81} \)

Irrational:

• \( \pi \)
• \( 2\sqrt{2} \)