A rational number is any number that can be written as a fraction:

ab\frac{a}{b}ba​

where:

• a and b are integers (whole numbers like -3, 0, 7)

• b cannot be 0 (because you can’t divide by 0)

So if a number can be written as a fraction, it is rational.

⭐ Examples of Rational Numbers

1) Fractions

These are automatically rational:

• 3/4 ​

• −5/2​

• 10/7​

2) Whole Numbers

All integers are rational because you can write them as fractions over 1:

• 6 = 6/1​

• −9 = −9/1​

• 0 = 0/1​

3) Terminating Decimals

Decimals that end are rational because they can be written as fractions:

• 0.5 = 1/2 ​

• 2.75 = 11/4​

• −3.2 = −16/5​

4) Repeating Decimals

Decimals that repeat forever are also rational:

• 0.333… = 1/3​

• 0.666… = 2/3​

• 1.272727… = 14/11​

❌ What Is NOT a Rational Number?

Numbers that cannot be written as a fraction are called irrational numbers.

Examples:

• π = 3.141592… (never ends, never repeats)

• sqrt{2} = 1.414213… (never ends, never repeats)

🧠 Key Idea to Remember

A number is rational if its decimal form:
✅ terminates (ends)
OR
✅ repeats (has a repeating pattern)