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This essential trains for: SAT-I, GMAT, AMC-8, AMC-10, AMC-12, Math Kangaroo 5-6, Math Kangaroo 7-8, Math Kangaroo 9-10.

Decimals are of several kinds. Only those that represent rational numbers can be written in fractional form.

Nature of Number Type of Decimal Example Conversion rule
rational terminating equation equation

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rational non-terminating, repeating equation equation
rational non-terminating, mixed equation equation

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irrational non-terminating, non-repeating equation cannot be converted to a fraction

Convert repeating decimals to fractions:

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Multiply the number by a power of 10 equal to the number of repeating digits:

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Convert mixed decimals to fractions:

Multiply the number by a power of 10 equal to the number of repeating and non-repeating digits:

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Therefore, the rule is: take the number formed by the fixed and repeating parts, subtract the number formed by the fixed part from it and divide by a number formed with as many nines as digits in the repeating part followed by as many zeros as digits in the fixed part.

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