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# Representing Rational Numbers on a Number Line

All the rational number can be represented on number line, it is an image of Straight Line and it has a range from negative (-ve) infinity to Positive (+ve) infinity. On number line generally the Point indicated as Integer but we can simply convert them in to the Rational Numbers by just dividing the space between integer. With the help of number line we can find the Position of any rational number in number line. Number line can be represented as:

Now, we can see that in above number line all the values at right side are positive values and values at left side are negative values. Example: find the position of 2/7 on number line? 2/7 is a positive value so it will be in the right side of 0 , for simpler calculation we need to convert it to Decimals then it becomes easier to find the position of the given number. 2/7 can be written in decimals as '0.285' now, we need to find the position of 0.285. '0.285' is bigger than zero and less than one. To find exact value we will divide the portion between 0 and 1 then we will get the exact position of 0.5. After finding the position of 0.5 we just need to divide it again in to half to get the exact position of 0.250 as we are 0.250 is very close to 0.285 so we can conclude that 0.285 is near to number line as 0.285 is bigger than 0.250 so it will be in the right side of the number line in this way we can get the position of any rational number.

Note:

For representing rational and irrational numbers in mathematics, we use number line. A number line is graphical representation of numbers from negative infinity to positive infinity in a single line. For drawing number line we use following steps–

Step1. First of all we draw a horizontal straight line because in generally all number lines are represented as a horizontal line.

Step 2: Number line represents negative infinity to positive infinity, so we draw directions at both side of horizontal line.

Step 3: From negative infinity to positive infinity, we represent 0 as an origin point because 0 is a mid point.

Step 4: After this we write all positive values on the right side of 0 and all negative sides on the left side of 0.

Step 5: Here marking on number line is not fix, it depend on students because if student giving the answer of any integer, they mark all integers on number line with 1,2....... or 2,4,6........It’s their choice how they mark number on number line.

Now we take some examples which represent different-different marking approaches of students -

Example 1: Represent 4/5 on number line.

Solution: For representation of 4/5 on number line, we use above steps:

here we represent all integer with 1,2,3,4.........form.

<----------------(-4)--(-3)--(-2)--(-1)--0--(4/5)--1--2--3--4--------------->

Example 2 : Represent -2/3 on number line.

Solution: We use above 5 steps to representing 2/3 on number line:

<----------------(-4)----(-2)--(-2/3)--0----2----4--------------->

Here we represent all integer with -2,0,2,4.........form.

These are some examples which tell that student use different-different marking approaches on number line. So, we can say that Line reference is not fixed it can be marked according to the students.

## Where the rational number 34/10 exists on number line?

34/10 can be written as 3.4 so the place of 3.4 in number line is between 3 and 4.