0.1 Repeating Times 100: Understanding the Concept
Introduction
When we multiply a decimal number by an integer, the result is often a straightforward calculation. However, things can get interesting when we multiply a repeating decimal by an integer. In this article, we'll explore what happens when we multiply 0.1 repeating by 100.
Understanding Repeating Decimals
Before we dive into the calculation, let's quickly review what a repeating decimal is. A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.1 repeating is a repeating decimal because it can be written as 0.111111... (where the sequence "1" repeats indefinitely).
Multiplying 0.1 Repeating by 100
Now, let's multiply 0.1 repeating by 100. When we do this, we get:
0.1 repeating × 100 = 10
But how did we get this result? To understand this, let's break it down step by step:
- 0.1 repeating = 0.111111... (repeating sequence of "1")
- Multiply by 100: 0.111111... × 100 = 11.111111... (repeating sequence of "11")
As you can see, the result of multiplying 0.1 repeating by 100 is indeed 10. But why did the repeating sequence change from "1" to "11"?
The Reason Behind the Result
The key to understanding this result lies in the way we perform multiplication with repeating decimals. When we multiply a repeating decimal by an integer, the repeating sequence gets multiplied by that integer. In this case, the sequence "1" gets multiplied by 100, resulting in a sequence of "11".
Conclusion
In conclusion, multiplying 0.1 repeating by 100 results in 10. This might seem counterintuitive at first, but it's all about understanding how repeating decimals work when we multiply them by integers. Remember, the repeating sequence gets multiplied by the integer, resulting in a new sequence that might look different from the original one.
