Answer:
Explanation:
To write the recurring decimal 2.3181818... as a mixed number, we need to identify the repeating pattern and convert it into a fraction.
The recurring pattern in the decimal is 18. Therefore, we can represent the decimal as follows:
2.3181818... = 2 + 0.31(18)
To convert the repeating decimal into a fraction, we let x be the recurring pattern:
x = 0.31(18)
Multiplying both sides by 100 to eliminate the decimal point:
100x = 31.8181818...
Subtracting the original equation from this new equation, we can eliminate the recurring part:
100x - x = 31.8181818... - 0.3181818...
Simplifying:
99x = 31.5
Dividing both sides by 99:
x = 31.5 / 99
= 0.3181818...
Now, we can write the original decimal as a mixed number:
2 + 0.31(18) = 2 + x = 2 + 0.3181818...
To convert the fraction x into a mixed number, we can express it as a simplified fraction:
x = 0.3181818... = 31.5 / 99
Simplifying the fraction:
31.5 / 99 = 10 / 99 * 3.15
Therefore, the recurring decimal 2.3181818... can be expressed as the mixed number:
2 + (10 / 99 * 3.15)= 2+31.5/99