Compare and contrast the decimal representations of irrational numbers with the decimal representations of rational numbers give examples?

Question

Compare and contrast the decimal representations of irrational numbers with the decimal representations of rational numbers give examples?

Answer 1

The decimal representation of a rational number will eventually go into an infinite repeating pattern. For example, 9/22 = 0.409090909... . Some rational numbers have a decimal representation that terminates, but that can also be thought of as an infinite repeating pattern; for example, 2/5 = 0.40000000... .



An irrational number's decimal representation goes on forever without repeating. The square of 17 is 4.1231056256... but you cannot predict the 1000th digit without calculating all the digits in between.

Answer 2

Irrational numbers have a decimal representation that goes on forever and *never* repeats in a pattern.



For example;

π = 3.141592653589793...

e = 2.718281828459045...

√2 = 1.41421356237...



Rational numbers will either terminate outright, or end in an endless repeating pattern.



For example:

1/4 = 0.25

7/10 = 0.7

1/6 = 0.166666...

23/99 = 0.232323...

Answer 3

Irrational decimal representations go on infinitely in a way that is hard to predict

✓2=1.414 ...

e=2.71 ...

π=3.14 ...

Rational decimal representations usually repeat themselves:

3/2=1.5000 ...

2/3=0.6666 ...