0.1 Recurring and 5 Recurring as a Fraction
Recurring decimals, also known as repeating decimals, are decimal numbers that have a sequence of digits that repeats indefinitely. In this article, we will explore two recurring decimals: 0.1 recurring and 5 recurring, and learn how to convert them into fractions.
What is 0.1 Recurring?
0.1 recurring, also written as 0.111... or 0.1~, is a recurring decimal where the digit 1 repeats indefinitely. This decimal representation is equivalent to the fraction 1/9.
Converting 0.1 Recurring to a Fraction
To convert 0.1 recurring to a fraction, we can use the following steps:
- Let x = 0.111... (0.1 recurring)
- 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
Therefore, 0.1 recurring is equal to the fraction 1/9.
What is 5 Recurring?
5 recurring, also written as 5.555... or 5.~, is a recurring decimal where the digit 5 repeats indefinitely.
Converting 5 Recurring to a Fraction
To convert 5 recurring to a fraction, we can use the following steps:
- Let x = 5.555... (5 recurring)
- Multiply both sides by 10 to get 10x = 55.555...
- Subtract x from both sides to get 9x = 50
- Divide both sides by 9 to get x = 50/9
Therefore, 5 recurring is equal to the fraction 50/9.
Conclusion
In conclusion, we have learned how to convert two recurring decimals, 0.1 recurring and 5 recurring, into fractions. By using simple algebraic steps, we can easily convert these recurring decimals into their equivalent fraction forms.
