Question

Mark the following rational numbers on the number line. \[\dfrac{3}{4}\]

Answer 1

Hint: Questions like these are pretty easy to understand and are simple to solve. We can solve these quickly and efficiently once we understand all the core concepts behind the problem. To proceed with this problem, we need to have some basic as well as to some extent advanced knowledge of concepts like rational and irrational numbers, fractions and the number systems. The number system in general extends from a negative infinity to a positive infinity. In this whole domain, we need to mark a particular point. First we need to narrow down our area of concern and then mark the given point.

Complete step by step answer:
Now we start off with the solution to the given problem by narrowing down our domain on the number line to mark the given point on it. We can clearly see that the rational point given here is positive or in other words it is greater than zero. So we can omit the negative half of the number system and look for it on the positive half. One thing we also notice here is that the given rational number is less than one. So we can continue our search on the number system in between zero and one. We also see that it is greater than half or \[\dfrac{1}{2}\] . We can now write that \[\dfrac{1}{2} < \dfrac{3}{4} < 1\] . Marking the point on the number line we get.

Note: In problems like these we need to be through with our idea of fractions, rational numbers and number systems. Here, we first need to narrow down our search and then mark our point accordingly. If we don’t narrow down our search area, then it will be very difficult to find out the exact place. In cases of irrational points or points like \[\dfrac{1}{3},\dfrac{1}{6}...\] etc., we need to mark an approximate point instead of an exact one.