To convert 2.56¯¯¯¯¯ to a fraction, first, we can note that the bar over the digits 56 indicates that these digits repeat infinitely.
Let's represent the repeating part, 56, as a variable, say x.
Then, we can write an equation to represent 2.56¯¯¯¯¯:
2.56¯¯¯¯¯ = 2 + x
To remove the decimal point, we can multiply both sides of the equation by 100:
100 * 2.56¯¯¯¯¯ = 100 * (2 + x)
256.56¯¯¯¯¯ = 200 + 100x
Since the digits after the decimal point repeat indefinitely, we can subtract the original equation from the multiplied equation to eliminate the repeating part:
100 * 2.56¯¯¯¯¯ - 2.56¯¯¯¯¯ = 256.56¯¯¯¯¯ - 2.56¯¯¯¯¯
99 * 2.56¯¯¯¯¯ = 256
Now, we can solve for x:
99 * x = 256
x = 256 / 99
Thus, 2.56¯¯¯¯¯ as a fraction is 256/99.
Convert 2.56¯¯¯¯¯
to a fraction
1 answer