Question

define and give an example of:
repeating decimal:
a decimal with one or more digits that
example— 0.\overline{3} (from \frac{1}{3} or) 0.88 (
decimal expansion:
the way a number is written as a
number, showin its value using tenths, hundre
example— \frac{3}{5} is 0.6 (termi
decima
square:

Explanation:

To define and give an example of "Square" (in the context of mathematics, specifically in the subfield of Algebra or Geometry, but here we'll focus on the basic definition of the square of a number):

Step 1: Define "Square" (of a number)

The square of a number \( n \) is the result of multiplying the number by itself, i.e., \( n\times n \) or \( n^{2} \). In geometric terms, the area of a square with side length \( s \) is also called the square of \( s \), calculated as \( s\times s = s^{2} \).

Step 2: Give an example

• Numerical example: Let's take the number \( 5 \). The square of \( 5 \) is \( 5\times5 = 25 \), or in exponent form, \( 5^{2}=25 \).
• Geometric example: Consider a square with a side length of \( 4 \) units. The area of this square (which is the square of the side length) is \( 4\times4 = 16 \) square units. So, the square of \( 4 \) (in terms of the side length of the square) is \( 16 \).

If we were to present just the definition and a simple numerical example concisely:

A square of a number \( n \) is \( n \times n \) (or \( n^2 \)). For example, the square of \( 3 \) is \( 3\times3 = 9 \) (or \( 3^2 = 9 \)). In geometry, the area of a square with side length \( s \) is \( s^2 \); e.g., a square with side \( 2 \) has area \( 2^2 = 4 \).

Answer:

• Definition: The square of a number \( n \) is the product of \( n \) multiplied by itself (\( n\times n \) or \( n^{2} \)). In geometry, it also refers to the area of a square with side length \( s \), calculated as \( s\times s = s^{2} \).
• Example: The square of \( 5 \) is \( 5\times5 = 25 \) (or \( 5^{2}=25 \)). For a square with side length \( 3 \) units, its area (the square of \( 3 \)) is \( 3\times3 = 9 \) square units.