Ace the BMAT 2025 – Unleash Your Biomedical Superpowers!

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Question: 1 / 400

Which fraction corresponds to the decimal 0.111?

1/8

1/10

1/9

The decimal 0.111 can be interpreted as a repeating decimal, specifically 0.111... , which continues indefinitely. To convert this decimal into a fraction, it's helpful to recognize that the digit "1" repeats endlessly.

To convert a repeating decimal like 0.111... into a fraction, one common method is to set it equal to a variable, say $ x $:

1. Let $ x = 0.111... $.

2. To eliminate the repeating part, multiply both sides of the equation by 10: $ 10x = 1.111... $.

3. Next, subtract the first equation from this new equation:

$ 10x - x = 1.111... - 0.111... $.

4. This simplifies to $ 9x = 1 $.

5. Dividing both sides by 9 gives $ x = \frac{1}{9} $.

Thus, the decimal 0.111... corresponds to the fraction 1/9. Recognizing the nature of repeating decimals is key in understanding how to convert between decimal and fractional form effectively.

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