0.12 Repeating Times 100: Understanding the Concept
Have you ever wondered what happens when you multiply a repeating decimal by a whole number, like 0.12 repeating times 100? In this article, we'll explore the concept of repeating decimals and how to perform this seemingly complex operation.
What are Repeating Decimals?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12 is a repeating decimal because the sequence "12" repeats indefinitely: 0.121212... . You can see that the pattern "12" repeats over and over again.
How to Multiply a Repeating Decimal by a Whole Number
Now, let's get back to our original question: what happens when you multiply 0.12 repeating by 100? To perform this operation, we need to follow a few simple steps:
Step 1: Convert the Repeating Decimal to a Fraction
To multiply a repeating decimal by a whole number, we first need to convert the repeating decimal to a fraction. To do this, we can use the following formula:
Let x = 0.12 (repeating)
Multiply both sides by 100:
100x = 12.12 (repeating)
Subtract x from both sides:
99x = 12
Divide both sides by 99:
x = 12/99
So, the fraction equivalent of 0.12 repeating is 12/99.
Step 2: Multiply the Fraction by the Whole Number
Now that we have the fraction equivalent, we can multiply it by 100:
(12/99) × 100 = (12 × 100) / 99
Step 3: Simplify the Result
Finally, we simplify the result:
(12 × 100) / 99 = 1200 / 99
The Final Answer
So, 0.12 repeating times 100 is equal to 1200/99 or 12.12 (repeating).
Conclusion
Multiplying a repeating decimal by a whole number might seem daunting at first, but by following these simple steps, you can easily perform the operation. Remember to convert the repeating decimal to a fraction, multiply the fraction by the whole number, and simplify the result to get the final answer. With practice, you'll become more comfortable working with repeating decimals and whole numbers.
