# Can measurements be made more precise then the measuring device?

• mrspeedybob
In summary, the conversation discusses the use of a measuring device with a resolution of 1 and an accuracy of +/-1 to measure a quantity X. It is suggested that by making repeated measurements, an accuracy of +/- 0.5 can be achieved. However, the question is raised if any greater certainty can be achieved. The book "An Introduction to Error Analysis" by John Taylor is recommended for further understanding of this topic.
mrspeedybob
Suppose there is a quantity X to be measured. To do this you have a measuring device with a resolution of 1 and an accuracy of +/-1. It is imediately obvious that repeated measurements can yield an accuracy of +/- 0.5 but can any greater certainty be achieved?

If 2 measurements are made and they are, for example 6 and 7, then it can be stated that 5<=X<=7 for the first measurement and 6<=X<=8 for the second so 6<=X<=7 so X=6.5 +/- 0.5. What if 10 measurements were made and 9 came up 6 but only 1 came up 7. Can it be stated with any degree of certainty that X is closer to 6 then to 7?

"An Introduction to Error Analysis" by John Taylor is a good book.

If you can characterize the error of the instrument, perhaps something more specific than it has an accuracy of +/-1, then averaging the measurements can give you significantly more accuracy. The book describes it all. If you are interested in this subject it should be a fascinating read.

## 1. Can measurements be made more precise than the measuring device?

While measuring devices are designed to provide accurate and precise measurements, there are certain techniques and methods that can be used to improve the precision of measurements. This includes using multiple measuring devices and taking multiple readings, using statistical analysis to calculate the average measurement, and using more sensitive or advanced measuring devices.

## 2. How can we improve the precision of measurements?

As mentioned before, there are various ways to improve the precision of measurements. These include using multiple measuring devices, taking multiple readings, and using more sensitive or advanced measuring devices. Additionally, ensuring proper calibration and maintenance of the measuring device can also help improve its precision.

## 3. Is it possible to make measurements more precise without using advanced or expensive measuring devices?

While advanced or expensive measuring devices may provide more precise measurements, it is possible to improve the precision of measurements without them. This can be achieved by using statistical analysis, taking multiple readings, and ensuring proper calibration and maintenance of the measuring device.

## 4. Can human error affect the precision of measurements made with a measuring device?

Yes, human error can have an impact on the precision of measurements made with a measuring device. This can be due to incorrect usage, improper calibration, or inconsistent technique while taking measurements. It is important for the user to follow proper procedures and techniques to minimize human error and improve the precision of measurements.

## 5. Are there any limitations to how precise measurements can be with a measuring device?

While there are techniques to improve the precision of measurements, there are also limitations to how precise measurements can be with a measuring device. These limitations can vary depending on the type and quality of the measuring device, as well as external factors such as environmental conditions. It is important to understand the limitations of the measuring device and use proper techniques to achieve the most accurate and precise measurements possible.

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