hey can anyone help me with understanding what makes a number rational
and irrational
2 answers
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
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
1 answer