Draw a picture showing the markings (graduations) on...

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible). a. $128.7 \mathrm{~mL}$ b. $18 \mathrm{~mL}$ c. $23.45 \mathrm{~mL}$ If you made the measurements of three samples of water and then poured all of the water together in one container, what total volume of water should you report? Support your answer.

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible).
a. $128.7 \mathrm{~mL}$
b. $18 \mathrm{~mL}$
c. $23.45 \mathrm{~mL}$
If you made the measurements of three samples of water and then poured all of the water together in one container, what total volume of water should you report? Support your answer.

Key Concepts

Volume Summation

Volume summation involves adding together measured volumes, and it requires careful attention to the precision of each measurement. When combining measurements, the final total should be reported in a manner that reflects the precision of the least precise measurement. This ensures that the reported total volume does not imply a degree of accuracy beyond that provided by the original measurements.

Significant Figures

Significant figures represent the digits in a measurement that contribute to its precision. They not only include the certain digits but also the first uncertain digit. When recording volumes, the number of significant figures reflects the instrument’s precision. For example, values like 128.7 mL and 23.45 mL suggest different levels of precision, which in turn affect how calculations, such as the addition of volumes, should be appropriately reported to avoid implying unwarranted accuracy.

Graduated Markings

Graduated markings are the lines and numbers inscribed along a piece of glassware that allow the user to measure liquid volumes. These markings must be spaced at intervals that reflect the desired measurement precision, ensuring that the volumes drawn can be read accurately. The design of these graduations is crucial because it informs the user of how much liquid is present between the marks, allowing for consistent and reproducible measurements.

Measurement Precision

Measurement precision refers to the degree of refinement in the readings provided by the instrument, which is determined by the smallest increment (or graduation) that can be measured on the device. A finer graduation implies a higher precision and allows for smaller volume measurements. Understanding this concept is important because it affects how accurately one can measure, record, and later combine different volumes while taking into account the potential margins of error.

Transcript

00:01 Okay, so this problem is, um, related to being able to look at some kind of an experimental setup that involves measuring out some kind of liquid using graduated cylinders on being able to make precise measurements.

00:16 Right.

00:17 So we're asked to draw pictures showing the graduations or the markings of a graduated cylinder that would, um, measure out certain that'll be most accurate and measuring out certain volumes.

00:31 Um, so for the first volume, um, so as i'm writing these values down, let me remind you how we read graduated cylinder markings, right? so whenever the marking is on, the graduates owned or whatever place in terms off the numerical place value in the last digit off the number, um means that that is the most accurate.

00:59 That is the last accurate value that we can confidently determine.

01:02 And the graduated cylinder using the graduated cylinder, right? so, for example, um, let's start with b, because 18 is nice round number.

01:11 That would mean that this marking here, um or at least the marking close to it is 18 millimeters.

01:19 We can't really accurately tell you what the value of the 10th places because the markings, let's say only go by ones.

01:30 So because of that, we know that the answer is probably close to 18.

01:34 But it could be 18.1.

01:36 It could be 17.9.

01:38 We don't know, right? so then you have to draw your markings to illustrate that, um, the last place in the number.

01:46 So in 18 mills, it's the ones place that is, um, that place is shown that that that place with one's place is the difference between each marking on the graduates.

02:01 You'll notice that i separated each marking by the value off one.

02:04 Um, so it goes 17 18 19.

02:08 It goes by ones because the ones place is the last value that we're confident about in the measurement of the number.

02:17 Um, right.

02:19 So it could be 18 milliliters plus or minus 0.1 millimeter.

02:28 Let's say that's just a example.

02:29 I'm not actually sure what the actual error is on the graduate its own there, right? but that's that's a possibility of some one certainty in our measurement.

02:36 So similarly, let's go to a right.

02:39 So this value is probably close to 128.7 mills, which means that they're confident in the measurement up to the 10th place, which means that our graduations, if we're zoomed in on this graduated cylinder, um they're marking down here probably goes to 128.6 is a big graduates owner, and the one up here goes to 128.8 mills...

Please give Ace some feedback