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# Find 5 rational numbers between 1 and 2. We can approach this problem in at least two ways.

Last updated date: 16th Sep 2024
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Hint: A rational number is a number which can be expressed in the form $\dfrac{a}{b}$ where a and b are integers and $b\ne 0$ .
Rational numbers are either terminating or non-terminating and repeating in decimal form.
e.g. 3.4, 5.7777... = $5.\bar{7}$, 8.13 etc.
A number Z, which is greater than X and smaller than Y, is said to be between X and Y.

The numbers 1 and 2 have a denominator 1 and can be written as $\dfrac{1}{1}$ and $\dfrac{2}{1}$ respectively.
$\dfrac{1}{1}=\dfrac{1\times 10}{1\times 10}=\dfrac{10}{10}$ and $\dfrac{2}{1}=\dfrac{2\times 10}{1\times 10}=\dfrac{20}{10}$ .
Now, using the properties of numbers, we find that $\dfrac{11}{10},\dfrac{12}{10},\dfrac{13}{10},\dfrac{14}{10},\dfrac{15}{10}$ etc. are all between $\dfrac{10}{10}$ and $\dfrac{20}{10}$ .
$0.\bar{9}$ and 1 are not distinct numbers, they are equal.