Convert 2.56¯¯¯¯¯ to a fraction
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.
To convert the repeating decimal 2.56¯¯¯¯¯ to a fraction, we can set it up as follows:
Let x = 2.56¯¯¯¯¯
Multiply both sides of the equation by 10 to get rid of the repeating decimal:
10x = 25.6¯¯¯¯¯
Since there is one digit repeating after the decimal point, we can subtract the original equation from the multiplied equation:
10x - x = 25.6¯¯¯¯¯ - 2.56¯¯¯¯¯
9x = 23.04
Now, we can simplify the equation by dividing both sides by 9:
9x/9 = 23.04/9
x = 23.04/9
Therefore, the fraction equivalent of 2.56¯¯¯¯¯ is 23.04/9.