Question

Convert 2.56¯¯¯¯¯ to a fraction

Answer 1

To convert 2.56¯¯¯¯¯ to a fraction, we can use the following steps:

Step 1: Let's assign a variable to the repeating part of the decimal. In this case, let's use "x".

Step 2: Write an equation to represent the decimal as a fraction. Since the decimal part is repeating indefinitely, we multiply both sides of the equation by a power of 10 to move the decimal point. The equation becomes: 10x = 2.56¯¯¯¯¯.

Step 3: Subtract the original equation from the current equation to eliminate the repeating part: 10x - x = 2.56¯¯¯¯¯ - 0.56¯¯¯¯¯. Simplifying, we get 9x = 2.

Step 4: Solve for "x" by dividing both sides of the equation by 9: x = 2/9.

Step 5: Add the repeating part to the non-repeating part of the decimal to obtain the fraction: 2 + 2/9 = 20/9.

Therefore, 2.56¯¯¯¯¯ is equal to the fraction 20/9.