Now we'll work with a Vernier caliper. The way this works is that there is again an upper and lower scale. Here this is the centimeters 0, 1, 2, 3 on this axis here. Then the upper we have inches which we're going to neglect for our use. And then this is the lower scale down here is 0, 1, 2, 3 up to 9. And then 0 again is the minor scale. When it's shut, the Vernier caliper isn't measuring anything that is then the 0's on the major and minor axes line up. So we can see that this 0 on the minor scale and this on the major scale they line up quite well. And you'll notice no where else does that occur that is the markings on the minor and major scale line up. Except again at 0 here and there. We'll put our measurement object here between the teeth of the Vernier scale. And we'll close it. When we're measuring something there's a flat side here. And we'll want to put our device in that and then close it with a little bit of pressure. And then with that value we're going to see what the measurement is. On the major scale it's the question of where does the 0 on the minor scale line up with the major scale. So here we have a 0 on the minor scale which is a little past this hash mark here. So that's 5, 6, 7. It's a little more than 0.7 centimeters. The question is how much more than 0.7 centimeters is it? Since the 0 here doesn't line up with the major scale exactly we need to find where on the minor scale it does. So there's no match here until we reach say the 6 value. So on the minor scale the 6 mark lines up pretty well. You could even say the 7 mark lines up better. So we'll take this 7 as our minor scale measurement. Now the question is how do we combine this 0.7 centimeter measurement on the major scale with the 7 mark on the minor scale. The answer to that is over on the far side of our caliper there's a little marking that says 0.05 millimeters. This tells us the smallest unit of measurement for the caliper. So now when we look back this 0 on the minor scale is somewhere between 0.7 and 0.8 on the major scale. So this gives us some confidence that our measure is correct. Now that we know the smallest unit of measure on the minor scale is 0.05 millimeters that tells us what this 7 means. Each of these small marks from here to here is 0.05 millimeters. And so since this is 7 and then there are 2 marks per increment there are actually 14 of these small measurements. The way we'll combine these sets of measurements the 0.05 millimeters on the minor scale as the smallest measurement with the major scale of 0.7 centimeters is we'll take the major plus the number of minor increments in this case 14 and then multiply that number times the smallest measure. So what we get back after we convert to the correct units of centimeters in this case is 0.77 centimeters with an accuracy of plus or minus 0.005 centimeters. As a check this makes sense because the value should be between 0.7 centimeters and 0.8 centimeters. And if we look back at our original measurement we see that our 0 mark on the minor scale is close to the 0.8 so 0.77 centimeters makes sense. Now as an example of what happens if our scale is slightly different if we're using a different measure and we come up upon the case where the 0 on the minor scale lines up an increment on the major scale. For instance now I see that the 0 on the minor scale lines up very well with 1.7 on the major scale. What that does for our calculation is we still have a major scale of 1.7 centimeters but now our minor measurement is zero increments. And we multiply that times our smallest measure of 0.05 millimeters and what we get back is a more precise measure of 1.70 plus or minus 0.005 centimeters.