Convert into vulgar fraction:
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A.
371/900
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B.
299/121
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C.
4 11/90
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D.
4 11/99
Correct Answer:
C. 4 11/90
Explanation:
To convert the mixed recurring decimal 4.122... (where 11 is fixed and 90 repeats, though the context suggests 4.122... represents 4.1212... or similar recurring patterns), we follow the rule for converting mixed recurring decimals into vulgar fractions.1. First, identify the whole number, which is 4.
2. For the fractional part, the numerator is the difference between the number formed by all decimal digits (up to the end of the first repeating cycle) and the non-repeating digits. In the case of 0.122..., the numerator is 11 (from the sample 4 11/90).
3. The denominator is formed by writing as many nines as there are repeating digits, followed by as many zeros as there are non-repeating digits after the decimal point.
4. For the example 4 11/90, the fraction 11/90 represents the decimal 0.122... where 2 is the repeating digit.
5. Combining the whole number and the fraction gives 4 11/90. To express this as a single vulgar fraction, multiply 4 by 90 and add 11, resulting in 371/900.The correct choice is C, as 371/900 is the vulgar fraction equivalent of the recurring decimal provided in the context.
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