Question

Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Answer 1

Hint: We can list all the natural numbers from 102 and 113. Then we can find the prime numbers from it. Then we can count the number of natural numbers and prime numbers. We can find the required fraction given by dividing the number of prime numbers with the number of natural numbers.

Complete step-by-step answer:
We know that natural numbers are the counting numbers. It starts from 1 and goes to infinity.
The natural numbers from 102 to 113 can be written as,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.
Prime numbers are the numbers that have no other factor than one and the number itself.
The prime numbers from 102 to 113 are
103, 107, 109, 113.
Now we need to find the fraction of prime numbers.
We can count the prime numbers. After counting, we get the prime numbers is 4.
 Also, by counting, we get the number of natural numbers from 102 to 113 as 12.
The fraction of the prime numbers is given by dividing the number of prime numbers with the number of natural numbers in the given interval.
So, we can write the fraction as, \[\dfrac{4}{{12}} = \dfrac{1}{3}\]
Thus fraction of prime number is $\dfrac{1}{3}$

Note: Natural numbers are the set of all the positive integers from 1 to infinity. It is also called counting numbers as it is used for counting purposes. Natural numbers do not contain zero. The set of natural numbers along with zero is called whole numbers. Prime numbers are the numbers having no factors other than 1 and the number itself. The numbers which are not prime are called composite numbers. But 1 is neither prime nor composite. All the even numbers other than 2 are composite numbers as they are multiples of 2.