## Number Line Representation of Decimal Forms of Rational Numbers

This is a "fractal" referred to as "Mandelbrot Set". A fractal is a geometric representation which preserves its structure and design no matter how much you zoom in. Can you see in the above image how every smaller part of the image actually looks like the whole set?

Is this also what happens when we zoom in to a number line? Every tiny part of the line in structure resembles the whole line. So, can we say that a number line (or a straight line) is also a fractal? Let me know your thoughts in the discussion board below.

EXERCISE: Visualize 3.765 on the number line, using successive magnification.

GRAPHICAL REPRESENTATION of a RECURRING DECIMAL

A recurring decimal has a never ending decimal part. For this reason, it is not posible to determine its exact location on a number line.

For such numbers, we have two options:

1. We determine their position upto a finite number of decimal places, or

2. We express the decimal representation as the ratio of two integers, and then determine its exact location.

EXERCISE: Visualize $4.\overline{26}$ on the number line, up to 4 decimal places.

SELF PRACTICE: Visualize these numbers on the number line, up to 4 decimal places.

a)     $5.\overline{34}$

b)      $8.\overline{58}$.

c)     $7.\overline{09}$.

Discussion