Recurring Decimals: 0.14 Recurring and 0.2 Recurring in Simplest Form
In mathematics, recurring decimals are decimal numbers that have an infinite sequence of digits that repeat in a predictable cycle. In this article, we will explore two recurring decimals: 0.14 recurring and 0.2 recurring, and learn how to express them in their simplest form.
What is 0.14 Recurring?
0.14 recurring is a decimal number that has an infinite sequence of digits that repeat in a cycle of two digits: 14. It can be written as:
0.1414141414...
The sequence of digits "14" repeats indefinitely, making it a recurring decimal.
What is 0.2 Recurring?
0.2 recurring is a decimal number that has an infinite sequence of digits that repeat in a cycle of one digit: 2. It can be written as:
0.2222222222...
The digit "2" repeats indefinitely, making it a recurring decimal.
Converting Recurring Decimals to Fractions
Recurring decimals can be converted to fractions by using a simple formula. Let's convert 0.14 recurring and 0.2 recurring to their simplest fractions.
Converting 0.14 Recurring
Let x = 0.141414...
Since the sequence of digits "14" repeats, we can multiply both sides of the equation by 100 to get:
100x = 14.1414...
Subtracting x from both sides gives:
99x = 14
Dividing both sides by 99 gives:
x = 14/99
So, 0.14 recurring is equal to the fraction 14/99 in its simplest form.
Converting 0.2 Recurring
Let x = 0.222222...
Since the digit "2" repeats, we can multiply both sides of the equation by 10 to get:
10x = 2.222222...
Subtracting x from both sides gives:
9x = 2
Dividing both sides by 9 gives:
x = 2/9
So, 0.2 recurring is equal to the fraction 2/9 in its simplest form.
Conclusion
In this article, we learned about recurring decimals 0.14 recurring and 0.2 recurring, and how to convert them to their simplest fractions using a simple formula. By converting these recurring decimals to fractions, we can express them in a more compact and meaningful way, making it easier to perform mathematical operations and make calculations.
