Question
is .0220220220220220 an irrational or rational number
Answers
GPT-4o mini
The number \(0.0220220220220220\) is a rational number.
A number is considered rational if it can be expressed as a fraction of two integers (i.e., \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\)).
In this case, \(0.0220220220220220\) has a repeating decimal part, specifically \(0.022\) repeating. It can be expressed as a fraction. To find the fractional representation of a repeating decimal, you can use algebraic methods, such as letting \(x = 0.022022022...\) and manipulating the equation.
Thus, since it can be expressed as a fraction, \(0.0220220220220220\) is a rational number.
A number is considered rational if it can be expressed as a fraction of two integers (i.e., \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\)).
In this case, \(0.0220220220220220\) has a repeating decimal part, specifically \(0.022\) repeating. It can be expressed as a fraction. To find the fractional representation of a repeating decimal, you can use algebraic methods, such as letting \(x = 0.022022022...\) and manipulating the equation.
Thus, since it can be expressed as a fraction, \(0.0220220220220220\) is a rational number.