he number 0.555555... can be written as the fraction ____, and is a ____ number.
Responses
5/10 = 1/2; Rational
5/10 = 1/2; Rational
5/99; Irrational
5/99; Irrational
55/100 = 11/20; Irrational
55/100 = 11/20; Irrational
5/9; Rational
5/9; Rational
5/9
To find the fraction equivalent of the repeating decimal 0.555555..., we can use a simple trick. Let x = 0.555555... and multiply both sides of the equation by 10. This gives us 10x = 5.555555... Now, subtract the original equation from this new equation: 10x - x = 5.555555... - 0.555555.... Simplifying, we get 9x = 5.
Dividing both sides by 9, we find that x = 5/9. Therefore, the fraction equivalent of 0.555555... is 5/9.
Since the fraction can be expressed as the ratio of two integers, 5/9 is a rational number.