Question

Find three rational numbers between 2 and 3

Answer 1

multiply each by 4 2/1*4/4 = 8/43/1 * 4/4 = 12/4then 3 rational number between 2 and 3 are 9/4 10/4 and 11/4

Answer 2

Answer:

$\frac{9}{4} ,\:\frac{10}{4}\: and \: \frac{11}{4}\\\: are \:three\: rational\: numbers\\ \: between \: 2 \: and 3$

Step-by-step explanation:

We want three numbers,we write 2 and 3 as rational numbers with denominator 3+1 = 4

$i.e \:2\\ = \frac{2\times4}{4}\\=\frac{8}{4} --(1)$

$3\\ = \frac{3\times4}{4}\\=\frac{12}{4} --(2)$

Now,

$2=\frac{8}{4}<\big(\frac{9}{4},\frac{10}{4},\frac{11}{4}\big)<\frac{12}{4}=3$

Therefore,

$\frac{9}{4} ,\:\frac{10}{4}\: and \: \frac{11}{4}\: \\are \:three\: rational\: numbers\\ \: between \: 2 \: and 3$

Note :

There exist infinite number of rational numbers between any two given rational numbers.

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