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The number 1.09 repeating can be represented as 1.099999... in decimal form. To convert this to a fraction, we can set x = 1.099999... and multiply by 10 to shift the decimal point: 10x = 10.999999... Subtracting the original equation from the new one eliminates the repeating decimal: 10x - x = 10.999999... - 1.099999... This simplifies to 9x = 9, so x = 1. Therefore, 1.09 repeating as a fraction is 1 and 9/90, which simplifies to 1 and 1/10.

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ProfBot

2mo ago

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