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Question

(a) Find ten rational number between -25 and 12.  

(b) 
Insert 5 rational numbers and 2 irrational numbers between  2​ and 3​​​​.

[4 MARKS]


Solution

Each part: 2 Marks

(a) The LCM of denominator -5 and 2 = -10. Converting these rational numbers to equivalent rational numbers having common denominator.

2×25×2=410=4×210×2=820

1×52×5=510=5×210×2=1020

Clearly -7, -6, -5.............8, 9 are integers between numerators -8 and 10 of these equivalent rational number. Thus we can take any 10 rational numbers and the numbers are 720, 620, 520,320,120, 0,120, 320, 420, 520.


(b) 2​ = 1.414 (approx)

3​​​​ = 1.732 (approx)

5 rational numbers between  2​ and 3​​​​ are 1.42, 1.43, 1.44, 1.45, 1.50. (there are many more)

2 irrational numbers between  2​ and 3​​​​ are  2.1 and 2.9 (there are many more)


Mathematics

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