# Ratios containing zero

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.

• Maybe it is easier for you if you consider the 4D:2D ratio, which is always the reciprocal of the 2D:4D, for example for group A it is $\frac1{0.96}\approx 1.04$ and so no longer has that pesky zero – Hagen von Eitzen Feb 17 at 12:28

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.

• Thank you! This helps a lot – Michelle Feb 17 at 14:22