Convert 0.8¯¯¯ to a rational number

Answer 1

To convert the repeating decimal 0.8¯¯¯ (0.8888...) to a rational number, we need to define it as the sum of a terminating decimal and a fraction.

Let x = 0.8¯¯¯

Multiplying both sides of the equation by 10, we have:
10x = 8.8¯¯¯

Subtracting the original equation from this new equation eliminates the repeating part:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8

Now, we solve for x:
x = 8/9

Therefore, 0.8¯¯¯ is equal to the rational number 8/9.