can 0.8¯ be written as a fraction and why?
Yes, 0.8¯ can be written as a fraction. The line above the 8 (known as the vinculum) indicates that the digit 8 is repeated indefinitely. To convert this repeating decimal into a fraction, we set up an equation. Let x = 0.8¯ and multiply both sides of the equation by 10 to shift the decimal point:
10x = 8.888¯
Now, we subtract the original equation from the new equation to eliminate the repeating decimal:
10x - x = 8.888¯ - 0.8¯
Simplifying,
9x = 8
x = 8/9
Therefore, 0.8¯ can be written as the fraction 8/9.