Convert 0.8¯¯¯ to a rational number
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.
To convert 0.8¯¯¯ to a rational number, we can represent it as a fraction.
Let's consider x = 0.8¯¯¯.
To eliminate the repeating decimal, we multiply both sides of the equation by a power of 10 that is equal to the number of decimal places in the repeating part.
Since there is only one repeating digit, we multiply both sides by 10 to get rid of the repeating decimal:
10x = 8.8¯¯¯
Now, subtract the original equation from the equation we just obtained:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
This simplifies to:
9x = 8
To solve for x, divide both sides of the equation by 9:
9x/9 = 8/9
Simplifying further, we get:
x = 8/9
Therefore, 0.8¯¯¯ is equal to 8/9 when represented as a rational number.