Every irrational number can be expressed on the number line. This statement is

• always true
• never true
• true subject to some condition
• None of these

The statement that every irrational number can be expressed on the number line is true. Irrational numbers, such as the square root of 2 or pi, cannot be written as a simple fraction, but they can still be located on the number line. This is because the number line includes all real numbers, which encompasses both rational and irrational numbers.

Understanding the Number Line

The number line is a visual representation of numbers where:

• Rational numbers (like 1/2 or 3) are placed at specific points.
• Irrational numbers fill in the gaps between rational numbers.

Examples of Irrational Numbers

Some common examples include:

• √2 (approximately 1.414)
• π (approximately 3.14159)
• e (approximately 2.71828)

Each of these numbers can be found on the number line, demonstrating that they are indeed expressible in this format.