To determine what fraction of the natural numbers from 102 to 113 are prime, we first need to identify the prime numbers within this range.
The natural numbers between 102 and 113 are:
- 102
- 103
- 104
- 105
- 106
- 107
- 108
- 109
- 110
- 111
- 112
- 113
Now, we’ll check each of these numbers for primality:
- 102: Not prime (divisible by 2)
- 103: Prime
- 104: Not prime (divisible by 2)
- 105: Not prime (divisible by 3 and 5)
- 106: Not prime (divisible by 2)
- 107: Prime
- 108: Not prime (divisible by 2)
- 109: Prime
- 110: Not prime (divisible by 2 and 5)
- 111: Not prime (divisible by 3)
- 112: Not prime (divisible by 2)
- 113: Prime
The prime numbers in this range are: 103, 107, 109, and 113. This gives us a total of 4 prime numbers.
Now, there are a total of 12 natural numbers from 102 to 113. To find the fraction of these numbers that are prime, we use the formula:
Fraction of prime numbers = (Number of prime numbers) / (Total natural numbers)
So plugging in our numbers:
Fraction = 4 / 12 = 1 / 3
Therefore, the fraction of the natural numbers from 102 to 113 that are prime is 1/3.