State whether the following numbers are rational or irrational.

• a) 1.5
• b) √7
• c) 0.7̅
• d) 0.7̇3
• e) √121
• f) π

To determine if the given numbers are rational or irrational, we need to understand the definitions of both types of numbers.

Definitions

Rational numbers can be expressed as a fraction of two integers (where the denominator is not zero). In contrast, irrational numbers cannot be written as a simple fraction and have non-repeating, non-terminating decimal expansions.

Analysis of Each Number

• a) 1.5: This is a rational number because it can be expressed as 3/2.
• b) √7: This is an irrational number since it cannot be simplified to a fraction and its decimal form is non-repeating.
• c) 0.7̅: This represents the repeating decimal 0.777..., which is rational. It can be expressed as 7/9.
• d) 0.7̇3: This is a terminating decimal (0.73), which is rational and can be expressed as 73/100.
• e) √121: This is a rational number because it simplifies to 11, which is an integer.
• f) π: This is an irrational number as it cannot be expressed as a fraction and its decimal representation is non-repeating and infinite.

Summary

In summary:

• 1.5: Rational
• √7: Irrational
• 0.7̅: Rational
• 0.7̇3: Rational
• √121: Rational
• π: Irrational