0.1 Recurring and 2/3 as a Fraction: Understanding the Concept
In mathematics, recurring decimals and fractions are two fundamental concepts that are often used to represent rational numbers. In this article, we will explore the relationship between 0.1 recurring and 2/3 as a fraction, and how they are related.
What is 0.1 Recurring?
0.1 recurring, also known as 0.1 repeated or 0.1 infinity, is a decimal that has an infinite number of 1s after the decimal point. It is written as 0.111... where the dots represent the infinite repetition of the digit 1. This type of decimal is known as a recurring decimal or a repeating decimal.
What is 2/3 as a Fraction?
2/3 is a fraction that represents the division of 2 by 3. It is a way of expressing a part of a whole, where the top number (2) is the numerator, and the bottom number (3) is the denominator.
The Relationship Between 0.1 Recurring and 2/3
Now, let's explore the relationship between 0.1 recurring and 2/3 as a fraction. To do this, we need to convert 0.1 recurring into a fraction.
Converting 0.1 Recurring to a Fraction
To convert 0.1 recurring to a fraction, we can use the following method:
Let x = 0.111...
Multiply both sides by 10 to get:
10x = 1.111...
Subtract x from both sides to get:
9x = 1
Divide both sides by 9 to get:
x = 1/9
So, 0.1 recurring is equal to 1/9 as a fraction.
The Connection to 2/3
Now, let's see how 1/9 is related to 2/3.
To do this, we can multiply both the numerator and the denominator of 1/9 by 2 to get:
(2 x 1) / (2 x 9) = 2/18
Simplifying the fraction, we get:
2/18 = 1/9
Now, we can see that 1/9 is equivalent to 2/18. And, since 2/18 is the same as 1/9, we can conclude that 0.1 recurring is equal to 2/18, which is equivalent to 1/9.
Conclusion
In conclusion, 0.1 recurring and 2/3 as a fraction are related through the conversion of 0.1 recurring to a fraction, which is 1/9. We have seen how 1/9 is equivalent to 2/18, which is the same as 1/9. This relationship highlights the connection between recurring decimals and fractions, and demonstrates the equivalence of 0.1 recurring and 2/3 as a fraction.
