Adding Repeating Decimals: 0.14 Recurring + 0.2 Recurring
When dealing with repeating decimals, it can be challenging to perform arithmetic operations like addition. In this article, we will explore the process of adding two repeating decimals, specifically 0.14 recurring and 0.2 recurring.
What are Repeating Decimals?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.14 recurring is a repeating decimal because the sequence "14" repeats indefinitely: 0.14141414... Similarly, 0.2 recurring is a repeating decimal because the sequence "2" repeats indefinitely: 0.22222...
Adding 0.14 Recurring and 0.2 Recurring
To add 0.14 recurring and 0.2 recurring, we need to follow a few steps:
Step 1: Convert Repeating Decimals to Fractions
We can convert each repeating decimal to a fraction by dividing the repeating part by the number of digits in the repeating part.
- 0.14 recurring = 14/99 (since the repeating part "14" has 2 digits)
- 0.2 recurring = 2/9 (since the repeating part "2" has 1 digit)
Step 2: Add the Fractions
Now, we can add the fractions:
(14/99) + (2/9) = ?
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which is 99. We can rewrite the fractions with the LCM as the denominator:
(14/99) + (18/99) = 32/99
Step 3: Convert the Fraction Back to a Decimal
Finally, we can convert the fraction back to a decimal:
32/99 = 0.323232...
So, 0.14 recurring + 0.2 recurring = 0.323232... or 0.32 recurring.
Conclusion
Adding repeating decimals requires converting them to fractions, adding the fractions, and then converting the result back to a decimal. By following these steps, we can accurately add 0.14 recurring and 0.2 recurring to get 0.32 recurring.
