0.19 Repeating Decimal as a Fraction
Have you ever wondered how to convert a repeating decimal to a fraction? In this article, we'll explore how to convert the repeating decimal 0.19 to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, the decimal 0.19 is a repeating decimal because it can be written as 0.19191919... with the sequence "19" repeating forever.
Converting 0.19 to a Fraction
To convert the repeating decimal 0.19 to a fraction, we can follow these steps:
Step 1: Let x = 0.19
Let's start by letting x equal 0.19.
Step 2: Multiply both sides by 100
Next, we'll multiply both sides of the equation by 100, which gives us:
100x = 19.19
Step 3: Subtract x from both sides
Now, let's subtract x from both sides of the equation, which gives us:
99x = 19
Step 4: Solve for x
Finally, we can solve for x by dividing both sides of the equation by 99, which gives us:
x = 19/99
The Result
So, the repeating decimal 0.19 is equal to the fraction 19/99.
Why Does This Work?
This method works because multiplying both sides of the equation by 100 causes the repeating sequence "19" to shift over, allowing us to subtract x from both sides and solve for x. This is a general method that can be used to convert any repeating decimal to a fraction.
Conclusion
In this article, we learned how to convert the repeating decimal 0.19 to a fraction. By following these steps, we can convert any repeating decimal to a fraction. This is a useful skill to have in mathematics, and it can come in handy in a variety of situations.
