Question

A car tire is worn to $\dfrac{1}{16}th$ of an inch. How many centimetres is that?

Answer 1

Hint: Recall that inches and centimetres are both units of length. You can use a regular ruler to find the equivalence between centimetres and inches since they usually have measuring scales for both units. To this end, use the empirical relation for how many centimetres are in an inch to determine how many centimetres constitute $\dfrac{1}{16}th$ of an inch.
Formula Used:
$1\;inch = 2.54\;cm$

Complete answer:
We are given that a car tire is worn to $\dfrac{1}{16}th$ of an inch. This is equivalent to:
$\dfrac{1}{16} \times 1 = 0.0625\;inches$
Now, we need to determine how many centimetres the above measure corresponds to. For this we utilize the following conversion relation which follows that:
$1\;inch = 2.54\;cm$
Therefore, $0.0525\;inches$ will be equivalent to:
$0.0625 \times 2.54 = 0.15875\;cm$
Therefore, the care tire is worn by $0.15875\;cm$.

Note:
It is advisable to remember the conversion relation between $inch \rightarrow cm$ since it is fundamentally an empirical relation that cannot be mathematically derived. In case the conversion relations are a bit difficult to remember, simply take your regular $15\;cm$ or $30\;cm$ ruler which usually has markings in centimetres on one edge and inches on the opposite edge. Look at the marking corresponding to the $1\; inch$ mark on the centimetres side, which is usually at $\approx 2.5\;cm$.
Also, when using conversion factors, remember that the factor will always get multiplied with the measure when converting to a smaller unit and will always act like a divisor while converting the measure to a larger unit, since the larger unit usually encompasses multiple measures in smaller units.