Convert 0.5¯¯¯ to a fraction.

Answer 1

To convert a decimal recurring number to a fraction, we can use the following steps:

1. Let x be the recurring decimal number.
2. Write x in the form x = 0.¯¯¯¯¯¯¯¯¯¯¯¯¯a, where "a" represents the recurring digit(s).
3. Multiply both sides of the equation by 10^n (where n is the number of recurring digits) to eliminate the decimal part:
10^n * x = a.¯¯¯¯¯¯¯¯¯¯¯¯¯a
4. Subtract x from 10^n * x to eliminate the recurring part:
10^n * x - x = a.¯¯¯¯¯¯¯¯¯¯¯¯¯a - 0.¯¯¯¯¯¯¯¯¯¯¯¯¯a
<=> 10^n * x - x = a
5. Factor out x on the left side:
x * (10^n - 1) = a
6. Solve for x by dividing both sides of the equation by (10^n - 1):
x = a / (10^n - 1)

In the given case, we have 0.5¯¯¯¯¯¯¯¯¯ = 0.5. We can see that there is only one recurring digit, which is 5. Therefore, n = 1.

Using the formula from step 6, we can calculate the fraction:
x = 5 / (10^1 - 1) = 5 / 9

So, 0.5¯¯¯¯¯¯¯¯¯ is equal to the fraction 5/9.