Video Transcript
The zero value of a digital timer is 0.00 seconds. What is the resolution of the timer? (A) 1.00 seconds, (B) 0.10 seconds, (C) 0.01 seconds.
This question is asking us to determine the resolution of measurements provided by a timer, which measures time. The information we are given to answer this question is that the zero value of the timer is 0.00 seconds. What we mean by the zero value of the timer is that once we have turned the timer on but before we have started the timer to measure an interval of time, the value displayed on the timer is 0.00 seconds. There’s another useful way to think about this value using the language of measurement. Before we start the timer, the timer has been actively measuring for exactly zero seconds. So 0.00 seconds is the timer’s measurement of exactly zero seconds.
Now, one way to think about the resolution of a measuring device is as the smallest possible difference between two measured values. To be precise of course, we should mention that our two values must be different because any measuring device can have a difference of zero between two different measurements if those two different measurements return the same value. Returning to our timer, we know that we measured exactly zero as 0.00, which has two digits to the right of the decimal place. When we start the timer and the measured value begins to increase, the first digit to change will be the one farthest to the right, since that represents the smallest value that the timer can measure. In other words, a difference in the second digit to the right of the decimal point is the smallest difference between two measurements that can be displayed on this timer. But the smallest difference between two measured values is the resolution of the timer. So the resolution of the timer is a change in the second place to the right of the decimal point.
Looking at our answer choices, the one that shows the smallest possible change to the second place to the right of the decimal point is choice (C), 0.01 seconds. This is the resolution of the timer.
It’s worth taking a moment to understand what this resolution means practically when taking a measurement. Every measurement with nonzero resolution actually stands for an interval of possible exact values that produced that measurement. Using our timer as an example, the resolution is 0.01 seconds, which means that a measurement of, say, 1.00 seconds would be the result from any exact value between 0.995 seconds and 1.005 seconds. The fact that a range of exact values all produce the same measured value is exactly the source of the phenomenon of measurement uncertainty.
