Question

While measuring the length of a knitting needle, the reading of the scale at one end is $3cm$ and at the other end is $33.1cm$. What is the length of the needle?

Answer 1

Since a knitting is always in the form of a straight line, both the readings will be on a straight line. Therefore, the length of the needle will simply be the positive difference between the two readings.

Complete answer:
In the given case, the length of a knitting needle is being measured. To measure the length of the needle we can use any instrument that measures length. Let us simply say that the instrument used here is a ruler. We can measure the length of the needle by just keeping it on top of the scale.
It is said that one end of the needle reads $3cm$ and the other end of the needle reads $33.1cm$. Since a knitting is always in the form of a straight line, both the readings will be on a straight line.
This means that the first end of the needle is $3cm$ away from the $0cm$ mark on the scale and the second end is $33.1cm$ away from the $0cm$ mark. Therefore, the length of the needle will be $33.1-3=30.1cm$.

Hence, the length of the needle is $30.1\,cm$.

Note: We could find the length of the needle only because a needle represents a line segment. Therefore, we could find its length just by calculating the difference between the readings of the two ends. Since the needle is straight, we can think of the scale as the x-axis, where the coordinates are readings in centimetres (cm). Let the origin coincide with the $0cm$ mark of the scale. Then positions of the two ends of the needle will be ${{x}_{1}}=3cm$ and ${{x}_{2}}=33.1cm$ respectively.
The length of the needle will be equal to $l={{x}_{2}}-{{x}_{1}}$.
$l=33.1-3=30.1cm$.
Hence, the length of the needle is $30.1cm$.