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Find 8 rational numbers between 1 and 01

Answer»

Correct Question :

  • Find 8 rational numbers between -1 and 1

To Find :

  • 8 rational numbers between -1 and 1

Solution :

To find all the eight rational numbers in one step. Since we WANT eight numbers, we write -1 and 1 as rational numbers with denominators 8 + 1 = 9.

-1 can be WRITTEN as :

  • -1 × 9/9 = -9/9

1 can be written as :

  • 1 × 9/9 = 9/9

Then you can check that -8/9 , -7/9 , -6/9 , -5/9 , -4/9 , -3/9 , -2/9 , -1/9 , 1/9 , 2/9 , 3/9 , 4/9 , 5/9 , 6/9 , 7/9 , 8/9 are all the rational numbers between -1 and 1.

Therefore :

  • Eight rational numbers between -1 and 1 are -8/9 , -7/9 , -6/9 , -5/9 , 3/9 , 4/9 , 5/9 and 8/9 .

Remark :

  • Notice, you were asked to find eight rational numbers between -1 and 1 . But, you must have REALISED that in fact there are infinitely many Rational numbers between -1 and 1 . In general, there are infinitely many rational numbers between any two given rational numbers.

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