27/8 is a rational number right!! then what is its decimal form????
The correct answer and explanation is:
Yes, 27/8 is a rational number, and its decimal form is 3.375.
✅ Correct Answer:
27 ÷ 8 = 3.375
🧠 Explanation (300 words):
A rational number is defined as any number that can be expressed as a fraction of the form a/b, where a and b are integers, and b ≠ 0. Since 27 and 8 are both integers and 8 is not zero, 27/8 is clearly a rational number.
To convert 27/8 into its decimal form, we perform long division or use a calculator:
- 8 goes into 27 three (3) times:
8 × 3 = 24
Subtract: 27 − 24 = 3 - Bring down a decimal point and a zero (making it 30).
8 goes into 30 three (3) times:
8 × 3 = 24
Subtract: 30 − 24 = 6 - Bring down another zero (making it 60).
8 goes into 60 seven (7) times:
8 × 7 = 56
Subtract: 60 − 56 = 4 - Bring down another zero (making it 40).
8 goes into 40 five (5) times:
8 × 5 = 40
Subtract: 40 − 40 = 0
Now there’s no remainder, which means the division terminates, and the decimal form is 3.375.
🔍 Why This Matters:
Understanding the decimal form of a rational number is important in math and real-life applications. Rational numbers may have:
- Terminating decimals (like 3.375)
- Repeating decimals (like 1/3 = 0.333…)
If a fraction has only 2 and/or 5 as prime factors in its denominator after simplification, its decimal will terminate.
Since 8 = 2 × 2 × 2, it satisfies this rule, so 27/8 has a terminating decimal.
✅ Summary:
- 27/8 is a rational number.
- Decimal form: 3.375
- It terminates because the denominator is a power of 2.