Converting 0.76666 to a Fraction
Have you ever wondered how to convert a repeating decimal to a fraction? In this article, we will explore how to convert 0.76666, a repeating decimal, to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.76666, the sequence "66" repeats indefinitely.
Converting 0.76666 to a Fraction
To convert 0.76666 to a fraction, we can use the following steps:
Step 1: Let x = 0.76666
Let's start by letting x = 0.76666.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 76.6666
Step 3: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
99x = 76.6666 - 0.76666
Step 4: Simplify the Equation
Simplifying the equation, we get:
99x = 75.9
Step 5: Divide by 99
Divide both sides of the equation by 99 to get:
x = 75.9 / 99
Step 6: Simplify the Fraction
Simplifying the fraction, we get:
x = 253/330
Therefore, 0.76666 as a fraction is 253/330.
Conclusion
In this article, we have successfully converted 0.76666, a repeating decimal, to a fraction. By following the steps outlined above, you can convert any repeating decimal to a fraction.
