The recurring decimal 0.84̅4 (where only 44 repeats) equals which fraction in lowest terms?

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38/45. Let x = 0.84̅4 (repeating). Rule for mixed recurring decimals: numerator = (all digits after the point) minus (the non-repeating digits). All digits after the point, read as one number, are 844. The non-repeating part alone is 8. Numerator = 844 - 8 = 836. The denominator has one 9 for each repeating digit (2) followed by one 0 for each non-repeating digit (1), giving 990. So x = 836/990. The H.C.F. of 836 and 990 is 22. Dividing both parts by 22 gives 38/45 = 38/45. Check: 38/45 written as a decimal reproduces 0.84̅4.

The recurring decimal 0.84̅4 (where only 44 repeats) equals which fraction in lowest terms?

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