0.14 Recurring + 0.2 Recurring as a Fraction
In mathematics, recurring decimals are decimal numbers that have a repeating pattern of digits. In this article, we will explore how to add two recurring decimals, 0.14 recurring and 0.2 recurring, and express the result as a fraction.
What is 0.14 Recurring?
0.14 recurring is a decimal number that has a repeating pattern of digits, specifically 14 repeating infinitely. It can be written as:
0.14141414...
What is 0.2 Recurring?
0.2 recurring is a decimal number that has a repeating pattern of digits, specifically 2 repeating infinitely. It can be written as:
0.22222222...
Adding 0.14 Recurring and 0.2 Recurring
To add 0.14 recurring and 0.2 recurring, we need to convert them into fractions first.
Converting 0.14 Recurring to a Fraction
To convert 0.14 recurring to a fraction, we can use the following formula:
x = 0.14141414... 100x = 14.14141414...
Subtracting x from 100x, we get:
99x = 14 x = 14/99
So, 0.14 recurring can be written as a fraction: 14/99
Converting 0.2 Recurring to a Fraction
To convert 0.2 recurring to a fraction, we can use the following formula:
x = 0.22222222... 10x = 2.22222222...
Subtracting x from 10x, we get:
9x = 2 x = 2/9
So, 0.2 recurring can be written as a fraction: 2/9
Adding the Fractions
Now that we have converted both numbers to fractions, we can add them:
14/99 + 2/9
To add these fractions, we need to find the least common multiple (LCM) of 99 and 9, which is 99. So, we can rewrite the fractions with a denominator of 99:
14/99 + 22/99
Now, we can add the fractions:
(14 + 22) / 99 = 36/99
Simplifying the fraction, we get:
4/11
Result
The result of adding 0.14 recurring and 0.2 recurring is 4/11.
In conclusion, we have successfully added two recurring decimals and expressed the result as a fraction.
