hey can anyone help me with understanding what makes a number rational
and irrational
https://www.mathsisfun.com/irrational-numbers.html
All decimals that can be written as a standard fraction represent rational numbers. (rational : from ratio)
That includes all whole numbers, and integers.
(any integer can be written as a fraction, e.g. 4 = 8/2 )
numbers whose decimals are non-repeating AND non-terminating are called irrational numbers.
e.g. 34.57557555755557.....
Of course numbers such as π, e, log 34, tan 56°, ... are irrational.
numbers with non-termination but repeating decimals are rational and can be converted to fractions.
e.g. .123232323.....
let x = .1232323....
multiply by 100, the length of the repeating decimal is 2 , so I multiply by 10^2 to shift the decimal 2 places.
100x = 12.32323232...
x = .1232323...
subtract them:
99x = 12.20000... = 12.2
x = 12.2/99 = 122/990 = 61/495
Of course! I can help you with understanding what makes a number rational or irrational.
A rational number is any number that can be expressed as the ratio (or fraction) of two integers, where the denominator is not zero. In other words, it can be written in the form p/q, where p and q are integers and q is not equal to zero. For example, 1/2, -3/4, and 5/1 are all rational numbers.
To understand whether a number is rational, you need to check if it can be expressed in the form p/q. If it can, then the number is rational. You can do this by simplifying the fraction. If the fraction can be simplified to its simplest form, it is rational. For example, the fraction 2/4 can be simplified to 1/2, so it is rational.
On the other hand, an irrational number is any number that cannot be expressed as a simple fraction or ratio of integers. Irrational numbers cannot be written as terminating or repeating decimals. Examples of irrational numbers include √2 (the square root of 2), π (pi), and e (Euler's number).
To determine if a number is irrational, you can try to express it as a fraction. If you cannot find two integers that can form a fraction equivalent to the given number, then it is irrational. For example, √2 cannot be expressed as a simple fraction, so it is irrational.
I hope this explanation helps! Let me know if you have any further questions.