0.1 Repeating as a Mixed Number
Introduction
In mathematics, a repeating decimal is a decimal representation of a number that exhibits a repeating pattern of digits. One such example is 0.1 repeating, also written as 0.111... or 0.1̄. But have you ever wondered how to convert this repeating decimal to a mixed number? In this article, we'll explore the process of converting 0.1 repeating to a mixed number.
What is a Mixed Number?
A mixed number is a combination of a whole number and a proper fraction. It is written in the form of a b/c, where a is the whole number part, b is the numerator, and c is the denominator. For example, 2 3/4 is a mixed number.
Converting 0.1 Repeating to a Mixed Number
To convert 0.1 repeating to a mixed number, we need to find the equivalent fraction. Let's use the following steps:
Step 1: Let x = 0.1̄
Let x be equal to 0.1 repeating.
Step 2: Multiply both sides by 10
Multiply both sides of the equation by 10 to get:
10x = 1.1̄
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
9x = 1
Step 4: Divide both sides by 9
Divide both sides of the equation by 9 to get:
x = 1/9
Step 5: Write as a Mixed Number
Since 1/9 is a proper fraction, we can write it as a mixed number:
0.1̄ = 1/9
Conclusion
In conclusion, 0.1 repeating can be converted to a mixed number by following the steps outlined above. The equivalent mixed number is 1/9. This process can be applied to convert any repeating decimal to a mixed number.
