Write two rational number between −2 and −1 full explanation
Answers
Answer:
Hint: The rational number between a and b is (a+b)2, use this equation to find the rational numbers between the given two numbers.
Complete step-by-step answer:
Given, to find 5 rational numbers between -2 and -1.
As, we know, the rational number between a and b is given by, (a+b)2
Hence, the rational number between -2 and -1 is (−2−1)2=−32=−1.5
Rational number between -2 and -3/2 is ⎡⎣⎢⎢⎢⎢−2+(−32)2⎤⎦⎥⎥⎥⎥=−74=−1.75
Rational number between -2 and -7/4 is ⎡⎣⎢⎢⎢⎢−2+(−74)2⎤⎦⎥⎥⎥⎥=−158=−1.875
Rational number between -2 and -15/8 is ⎡⎣⎢⎢⎢⎢−2+(−158)2⎤⎦⎥⎥⎥⎥=−3116=−1.9375
Rational number between -31/16 and -1 is ⎡⎣⎢⎢⎢⎢(−3116)−12⎤⎦⎥⎥⎥⎥=−4732=−1.46875
Therefore, five rational numbers between -2 and -1 are -1.75, -1.875, -1.9375, -1.46875, -1.5.
Note: Whenever such a type of question appears, i.e., it is asked to find a rational number between any two rational numbers, suppose x and y, the simplest approach is to divide their sum by 2, as mentioned in the question. Proceed step by step, obtain the value of (sum of the two no.)/2, then find the next rational number by dividing the sum of the first rational no. obtained in step 1 with the first number in the range, repeat it till you get all the required rational numbers.