0.1667 Repeating as a Fraction
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.1667, which is a repeating decimal. In this article, we will explore how to convert 0.1667 repeating as a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.1667 is a repeating decimal because the sequence "1667" repeats indefinitely. Repeating decimals can be converted to fractions, which is our goal in this article.
Converting 0.1667 Repeating to a Fraction
To convert 0.1667 repeating to a fraction, we can use the following steps:
Step 1: Write the repeating decimal as an equation
Let x = 0.1667 (repeating)
Step 2: Multiply both sides of the equation by 10,000
10,000x = 1,667.1667 (repeating)
Step 3: Subtract the original equation from the new equation
10,000x - x = 1,667.1667 - 0.1667 9,999x = 1,667
Step 4: Divide both sides of the equation by 9,999
x = 1,667 / 9,999 x = 1/6
Result
Therefore, 0.1667 repeating as a fraction is equal to 1/6.
Conclusion
In this article, we have successfully converted 0.1667 repeating to a fraction, which is 1/6. Repeating decimals can be converted to fractions using the steps outlined above. This skill is useful in various mathematical applications, including algebra and geometry.
