Convert 0.5¯¯¯ to a fraction.
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.
To convert the repeating decimal 0.5¯¯¯ to a fraction, we can follow these steps:
Step 1: Let x = 0.5¯¯¯.
Step 2: Multiply both sides of the equation by 10 to eliminate the repeating decimal:
10x = 5.5¯¯¯.
Step 3: Subtract the original equation from the one obtained in step 2 to eliminate the repeating part:
10x - x = 5.5¯¯¯ - 0.5¯¯¯,
9x = 5.
Step 4: Divide both sides of the equation by 9 to solve for x:
x = 5/9.
Therefore, the decimal 0.5¯¯¯ can be written as the fraction 5/9.