Question

using the black numbers on the stopwatch to answer the questions. what is the most accurate reading of seconds as indicated by the long second hand? look at the divisions between 2 and 4. what level of precision does this stopwatch have based on the divisions marked on its face?

Explanation:

Step1: Determine the value of each division

Looking at the stop - watch face, between the numbers \(2\) and \(4\) (black numbers), there are \(10\) divisions.
The range between \(2\) and \(4\) is \(4 - 2=2\) seconds.
If there are \(n = 10\) divisions in a range of \(R=2\) seconds, then the value of each division \(d=\frac{R}{n}\).

$$d=\frac{4 - 2}{10}=\frac{2}{10}=0.2$$

seconds.

Step2: Read the long - hand measurement

The long second - hand is at the \(6\)th division after \(2\).
The reading \(t\) is given by \(t=\text{lower bound}+(\text{number of divisions}\times\text{value per division})\)
The lower bound is \(2\) seconds, the number of divisions is \(6\), and the value per division is \(0.2\) seconds.

$$t = 2+(6\times0.2)=2 + 1.2=3.2$$

seconds

Answer:

The most accurate reading of seconds as indicated by the long second hand is \(3.2\) seconds. The stop - watch has a precision of \(0.2\) seconds (since each division between \(2\) and \(4\) (black numbers) is \(0.2\) seconds).