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Polynomials

Question

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Find six rational numbers between 3 and 4.

Solution

There can be infinitely many rational numbers between 3 and 4.

fraction numerator 3 plus 4 over denominator 2 end fraction equals 7 over 2 fraction numerator 3 plus begin display style 7 over 2 end style over denominator 2 end fraction equals 13 over 4 fraction numerator 3 plus begin display style 13 over 4 end style over denominator 2 end fraction equals 25 over 8 fraction numerator 3 plus begin display style 25 over 8 end style over denominator 2 end fraction equals 49 over 16 fraction numerator 3 plus begin display style 49 over 16 end style over denominator 2 end fraction equals 97 over 32 fraction numerator 3 plus begin display style 97 over 32 end style over denominator 2 end fraction equals 193 over 64

Thus, six ratonal numbers between 3 and 4 are

7 over 2 comma space 13 over 4 comma space 25 over 8 comma space 49 over 16 comma space 97 over 32 space and space 193 over 64

.
Alter

open table attributes columnalign right end attributes row cell 3 equals 3 over 1 equals fraction numerator 3 cross times 7 over denominator 3 cross times 7 end fraction equals 21 over 7 end cell row cell 4 equals 4 over 1 equals fraction numerator 4 cross times 7 over denominator 4 cross times 7 end fraction equals 28 over 7 end cell end table close curly brackets space 6 plus 1 equals 7

Thus, six rational numbers between 3 and 4 can be taken as

22 over 7 comma space 23 over 7 comma space 24 over 7 comma space 25 over 7 comma space fraction numerator 26 over denominator space 7 end fraction space and space 27 over 7.

Note. This is known as the method of finding rational numbers in one step.

Some More Questions From Polynomials Chapter

Find two rational numbers between 0.1 and 0.2.

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