0.5 Repeating as a Fraction
The decimal 0.5 repeating, also known as 0.5̄, is a recurring decimal that has an infinite number of repeating digits. But what is it in fractional form?
What is 0.5 Repeating?
0.5 repeating is a decimal that has a single digit, 5, that repeats indefinitely. It can be written as:
0.55555... (where the 5's go on forever)
Converting 0.5 Repeating to a Fraction
To convert 0.5 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.5̄
Let's say x = 0.5̄
Step 2: Multiply Both Sides by 10
Multiply both sides of the equation by 10 to get:
10x = 5.5̄
Step 3: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
9x = 5
Step 4: Divide Both Sides by 9
Divide both sides of the equation by 9 to solve for x:
x = 5/9
The Answer
Therefore, 0.5 repeating as a fraction is equal to:
5/9
So, the decimal 0.5 repeating is equivalent to the fraction 5/9.
Conclusion
In conclusion, we have successfully converted the decimal 0.5 repeating to a fraction. This fraction can be used in mathematical operations, making it easier to work with recurring decimals.
