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.
Convert 0.8¯¯¯ to a rational number
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