which of the following are terminating decimals 1)5/7 2)11/20 3)5/4 4)31/60
The Correct Answer and Explanation is:
The correct answers are:
2) 11/20 and 3) 5/4 are terminating decimals.
Explanation:
To determine if a fraction has a terminating decimal, you need to look at its denominator (after simplifying the fraction). A terminating decimal is a decimal that ends after a certain number of digits. For a fraction to terminate, the only prime factors of its denominator (after simplification) must be 2 and/or 5. These are the prime factors of 10, the base of our number system.
Let’s analyze each fraction:
1) 5/7
- Denominator = 7
- Prime factor: 7
- Since 7 is not 2 or 5, this fraction does not have a terminating decimal.
- Decimal form: 0.714285… (repeats)
Conclusion: Not terminating
2) 11/20
- Denominator = 20
- Prime factorization: 20 = 2² × 5
- All prime factors are 2 and 5.
- Decimal form: 0.55
Conclusion: Terminating
3) 5/4
- Denominator = 4
- Prime factorization: 4 = 2²
- Only prime factor is 2
- Decimal form: 1.25
Conclusion: Terminating
4) 31/60
- Denominator = 60
- Prime factorization: 60 = 2² × 3 × 5
- Contains 3, which is not allowed
- Decimal form: 0.51666… (repeats)
Conclusion: Not terminating
Final Answer:
11/20 and 5/4 are terminating decimals
5/7 and 31/60 are not terminating decimals because their denominators include prime factors other than 2 or 5.
