Ratios containing zero

Question

In one of our questions in school, we are asked,

For a given index finger length which of the following groups has the longest ring finger if the $2$D:$4$D ratio is:

Group A $0.96$,

Group B $0.98 $

Group C $0.99$ and

Group D $1.01$.

[Definition: $2$D:$4$D ratio means the ratio of the length of the index finger(2D) to ring finger (4D)]

The answer is Group A but I'm finding it very difficult to understand this especially with zeros involved in the ratios. I would be very grateful if someone could explain where the answer came from and how you got it. Thank you.

Answer 1

The $2D:4D$ ratio essentially represents $\frac{2D}{4D}$ , where $2D$ is the length of the index finger , and $4D$ is the length of the ring finger .

We are given that $2D$ is constant . Therefore , we have :-

For group A:- $\frac{2D}{4D} =0.96 \implies 4D = \frac{2D}{0.96}$

For group B:- $4D=\frac{2D}{0.98}$

For group C:- $4D=\frac{2D}{0.99}$

For group D:- $4D=\frac{2D}{1.01}$

Now recall that for a fraction $\frac{a}{b}$ , the greater the denominator $b$ , the smaller the fraction . The denominator is least in case of group A , and hence $4D$ is greatest , for group A.