1) Find a rational number between 7 and 8. Write your answer as a rational number.
2)Find a fractional number between 2 1/16 and 4 1/9.
3)Find an irrational number between 7 and 8. Explain your answer.
4) Find an irrational number between 2 ⅙ and 2 ½.
5) Find a rational number between 𝝅 and √12. Show your work.
Define) Irrational numbers on the numberline
Define) approximate
Define) Perfect squares
1) A rational number between 7 and 8 can be found by taking their average. The average of 7 and 8 is 7.5, which is a rational number.
2) To find a fractional number between 2 1/16 and 4 1/9, we can take their average. The average of 2 1/16 and 4 1/9 can be found by finding a common denominator: 2 9/144 and 4 16/144. Adding these, we get 6 25/144. Therefore, 6 25/144 is a fractional number between 2 1/16 and 4 1/9.
3) An irrational number between 7 and 8 can be found by taking the square root of a non-perfect square. For example, the square root of 7.2 is irrational because 7.2 is not a perfect square.
4) To find an irrational number between 2 1/6 and 2 1/2, we can take their average. The average of 2 1/6 and 2 1/2 can be found by finding a common denominator: 2 3/18 and 2 9/18. Adding these, we get 2 12/18, which simplifies to 2 2/3. Therefore, 2 2/3 is an irrational number between 2 1/6 and 2 1/2.
5) To find a rational number between π and √12, we can convert them to decimal form. π is approximately 3.14159, and √12 is approximately 3.4641. Taking their average, we get 3.302895. Converting this decimal to a fraction, we get 3391/1029. Therefore, 3391/1029 is a rational number between π and √12.
Definition of irrational numbers on the numberline: Irrational numbers are numbers that cannot be expressed as a fraction a/b, where a and b are integers and b is not equal to zero. They can be found between any two rational numbers on the numberline.
Definition of approximate: Approximate means to find a value that is close to the exact or precise value. It is an estimation or a close approximation of the real value.
Definition of perfect squares: Perfect squares are numbers that can be expressed as the square of an integer. For example, 1, 4, 9, 16, etc. are perfect squares because they can be obtained by squaring 1, 2, 3, 4, etc. respectively.