Question

Write any 10 rational numbers between 0 and 2.
(a) \[\dfrac{1}{10},\dfrac{2}{10},\dfrac{3}{10},\dfrac{4}{10},\dfrac{5}{10},\dfrac{6}{10},\dfrac{7}{10},\dfrac{88}{10},\dfrac{9}{10},\dfrac{10}{10}\]
(b) \[\dfrac{1}{10},\dfrac{2}{10},\dfrac{3}{10},\dfrac{4}{10},\dfrac{21}{10},\dfrac{6}{10},\dfrac{7}{10},\dfrac{8}{10},\dfrac{9}{10},\dfrac{10}{10}\]
(c) \[\dfrac{1}{10},\dfrac{2}{10},\dfrac{3}{10},\dfrac{4}{10},\dfrac{35}{10},\dfrac{6}{10},\dfrac{7}{10},\dfrac{8}{10},\dfrac{9}{10},\dfrac{10}{10}\]
(d) \[\dfrac{1}{10},\dfrac{2}{10},\dfrac{3}{10},\dfrac{4}{10},\dfrac{5}{10},\dfrac{6}{10},\dfrac{7}{10},\dfrac{8}{10},\dfrac{9}{10},\dfrac{10}{10}\]

Answer 1

Hint: There are countless rational numbers in between any two rational numbers. Check the given options and convert them into decimals. Now, observe every 10 rational numbers in each option to verify that whether they lie between 0 and 2 or not.

Complete step-by-step answer:

In mathematics, rational numbers are the numbers that can be represented as $\dfrac{p}{q}$, where $p$ and $q$ are integers and $q$ must not be equal to zero. If $q$ is equal to 1 then the given rational number will become an integer, that means, every integer is a rational number. In other words, a set of integers is the subset of a set of rational numbers. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over which is termed as non-terminating repeating decimal expansion.
Now, let us come to the question. We have to find 10 rational numbers between 0 and 2. On checking the options one-by-one after converting them into decimal we get,
In option (a) there will be a number 8.8 which does not lie between 0 and 2.
 In option (b) and (c) we have 2.1 and 3.5 respectively which does not lie between 0 and 2.
In option (d), when the rational numbers are converted into decimal we will get numbers like: 0.1, 0.2, 0.3,……., 1 and all of them lie between 0 and 2.
Hence, option (d) is the correct answer.

Note: We can also use another method in this question. As we can see that every option contains 10 in its denominator, so multiply the numbers in each option by 10 to get rid of the fraction. Now, we have to multiply 0 and 2 given in the question by 10 and then we have to find 10 rational numbers between 0 and 20. The answer will be the same as in the previous case, that is, option (d).