Re: 0.9999/1.0002 or 0.9998/1.0001
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15 Mar 2025, 01:56
We need to compare the value of $\(\frac{0.9999}{1.0002}\)$ with $\(\frac{0.9998}{1.0001}\)$ i.e. to compare $\(\frac{9999}{10002}\)$ with $\(\frac{9998}{10001}\)$
Since the denominators of the fractions are two consecutive numbers i.e. 1002 and 10001, they must be co-prime (Co-prime numbers are those which do not have any factor in common except 1).
Making their denominators same, we get the fractions as $\(\frac{9999 \times 10001}{10002 \times 10001}=\frac{99 \ldots . \ldots 8 \text { times. } \cdot 9}{10002 \times 10001}\)$ and
$$
\(\frac{9998 \times 10002}{10001 \times 10002}=\frac{99 \ldots 7 \text { times } \cdot .96}{10002 \times 10001}\)
$$
With same denominator fractions the comparison remains between their numerator values only and the fraction with higher numerator is greater.
Now clearly $\(999 \ldots 8\)$ times ... 9 is greater than $\(99 \ldots . .7$ tines.. 96\) , so is greater.
Hence column A has greater quantity, so the answer is (A).