Find an irrational number that is between 7.7 and 7.9. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth.
Answers
Answer:7.7
Step-by-step explanation:
An irrational number between 7.7 and 7.9 is 7.84487 . . .
Given: Two points 7.7 and 7.9 are given
To find: Irrational number between them
Solution: A rational number is expressed in form p/q where q is not equal to 0. A rational number is terminating or recurring. All real numbers other than rational numbers are irrational numbers.
A terminating decimal is a decimal that terminates after the decimal point. For example- 9/5 is a rational number because it is equal to 1.8 . Here the decimal terminates after the digit 8.
A recurring decimal is a decimal whose digits keep repeating after the decimal point. For example- 10/3 is a rational number because it is equal to 0.3333 . . Here, the digit 3 keeps repeating after the decimal point.
There are infinite irrational numbers between two points. One such point can be 7.84487 . . . Here, the digits do not terminate nor the same digits repeat after the decimal. Therefore, it is an irrational number.
On rounding the digits to the nearest hundredth(two digits after the decimal point), the number can be written as 7.84 .