Tell me whether each fraction. 1/n, is given as a terminating decimal or a repeating decimal for the given rules of n. Write t for terminating or r for repeating. It starts at 2- 10 which are t and r.
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Nilsa converted 1/12 to a repaeting decimal and wrote 0.083 as her answer what error did she make
i want the answers plss :))
To determine whether the fraction 1/n, where n is a given number, is a terminating or repeating decimal, we need to analyze the prime factorization of n.
1. For n = 2: The prime factorization of 2 is 2^1. The only prime factor is 2, which means that 2 is a prime number. In this case, 1/2 will result in a terminating decimal. Therefore, it is t.
2. For n = 3: The prime factorization of 3 is 3^1. The only prime factor is 3, which means that 3 is a prime number. In this case, 1/3 will result in a repeating decimal. Therefore, it is r.
3. For n = 4: The prime factorization of 4 is 2^2. The prime factorization includes 2 twice, which means that 4 is not a prime number. In this case, 1/4 will result in a terminating decimal. Therefore, it is t.
4. For n = 5: The prime factorization of 5 is 5^1. The only prime factor is 5, which means that 5 is a prime number. In this case, 1/5 will result in a repeating decimal. Therefore, it is r.
5. For n = 6: The prime factorization of 6 is 2^1 * 3^1. The prime factorization includes 2 and 3, which means that 6 is not a prime number. In this case, 1/6 will result in a repeating decimal. Therefore, it is r.
6. For n = 7: The prime factorization of 7 is 7^1. The only prime factor is 7, which means that 7 is a prime number. In this case, 1/7 will result in a repeating decimal. Therefore, it is r.
7. For n = 8: The prime factorization of 8 is 2^3. The prime factorization includes 2 three times, which means that 8 is not a prime number. In this case, 1/8 will result in a terminating decimal. Therefore, it is t.
8. For n = 9: The prime factorization of 9 is 3^2. The prime factorization includes 3 twice, which means that 9 is not a prime number. In this case, 1/9 will result in a repeating decimal. Therefore, it is r.
9. For n = 10: The prime factorization of 10 is 2^1 * 5^1. The prime factorization includes 2 and 5, which means that 10 is not a prime number. In this case, 1/10 will result in a terminating decimal. Therefore, it is t.
In summary:
1/2, 1/4, and 1/8 result in terminating decimals (t).
1/3, 1/5, 1/6, 1/7, 1/9, and 1/10 result in repeating decimals (r).