The number 0.555555... can be written as the fraction ____ and is a ____ number.
Responses
5/10 = 1/2; Rational
5/99; Irrational
55/100 = 11/20; Irrational
5/9; Rational
please help
The number 0.555555... can be written as the fraction 5/9 and is a rational number.
To find the fraction equivalent to the repeating decimal 0.555555..., we can use the concept of geometric series.
Step 1: Let's represent 0.555555... as x.
x = 0.555555...
Step 2: Multiply both sides of the equation by 10 to shift the decimal point one place to the right.
10x = 5.555555...
Step 3: Subtract the original equation (step 1) from the equation in step 2 to eliminate the repeating decimal portion.
10x - x = 5.555555... - 0.555555...
9x = 5
Step 4: Solve for x by dividing both sides of the equation by 9.
x = 5/9
So, the fraction equivalent to the repeating decimal 0.555555... is 5/9.
The answer to the question is:
The number 0.555555... can be written as the fraction 5/9 and is a rational number.