0.14285 Repeating as a Fraction
Have you ever wondered what 0.14285, a repeating decimal, looks like as a fraction? In this article, we'll explore how to convert this seemingly complicated number into a simple fraction.
The Basics of Repeating Decimals
Before we dive into converting 0.14285, let's quickly review what a repeating decimal is. A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In this case, the sequence "14285" repeats indefinitely to form the decimal 0.14285.
Converting 0.14285 to a Fraction
To convert 0.14285 to a fraction, we can use the following steps:
Step 1: Identify the repeating sequence
The repeating sequence in 0.14285 is "14285". Let's call this sequence "r".
Step 2: Create an equation
Let's create an equation using the repeating sequence:
$x = 0.14285\ldots$
Multiply both sides of the equation by 10^5 to get:
$10^5 x = 14285.14285\ldots$
Step 3: Subtract the two equations
Subtract the first equation from the second equation to get:
$10^5 x - x = 14285.14285\ldots - 0.14285\ldots$
This simplifies to:
$99999 x = 14285$
Step 4: Solve for x
Divide both sides of the equation by 99999 to get:
$x = \frac{14285}{99999}$
The Final Answer
So, 0.14285 as a fraction is:
0.14285 = 14285/99999
There you have it! The repeating decimal 0.14285 is equivalent to the fraction 14285/99999.
I hope this helps you understand how to convert a repeating decimal to a fraction. If you have any questions or need further clarification, feel free to ask!
