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. Write 2.3181818… as a mixed number.

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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

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