Convert 2.56¯¯¯¯¯

Question

to a fraction

Answer 1

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.