The number (which means ) is a rational number. Using algebra (let , multiply by 10, and subtract), explain why is exactly equal to 1.

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Let, x = = 0.9999… Multiplying both sides by 10 : ⇒ 10x = 9.9999… Subtracting the first equation from the second : ⇒ 10x - x = 9.9999... - 0.9999... ⇒ 9x = 9 ⇒ x = 1 So, = 1. This confirms that the recurring decimal is exactly equal to 1, not slightly less than 1. Although it may seem counter-intuitive, the infinite chain of 9's collectively equals 1. Hence, is exactly equal to 1.

Mathematics

The number (which means ) is a rational number. Using algebra (let , multiply by 10, and subtract), explain why is exactly equal to 1.

Whole Numbers

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