0.abbbbb as a fraction
The fraction form of 0.abbbbb can be written as a repeating decimal, where "abbbbb" indicates a repeating pattern of the digits.
To convert this to a fraction, we use the following method:
Let's call x = 0.abbbbb.
Then, if we multiply x by 10, we get 10x = abbbbbb.abbbbb.
Now, if we subtract the original equation (x = 0.abbbbb) from the new equation (10x = abbbbbb.abbbbb), we get:
10x - x = 9x = abbbbbb.abbbbb - 0.abbbbb
This simplifies to 9x = abbbbbb.
Now, we can solve for x by dividing both sides of the equation by 9:
x = abbbbbb / 9.
Therefore, the fraction form of 0.abbbbb is abbbbbb / 9.
To express the decimal number 0.abbbbb as a fraction, we can use the concept of repeating decimals. Let's represent the repeating part (bbbbb) as x:
x = abbbbb
To eliminate the repeating part, we can subtract the non-repeating part from the entire decimal:
10x = aabbbbb
Now, we can subtract the two equations to eliminate the repeating part:
(10x - x) = (aabbbbb - abbbbb)
9x = (a - 0) * 10 + (bbbb - b)
Simplifying further, we get:
9x = 10a + (bbbb - b)
Now, to express x as a fraction, we divide both sides of the equation by 9:
x = (10a + (bbbb - b)) / 9
Therefore, the fraction form of 0.abbbbb is (10a + (bbbb - b)) / 9.