# Uncertainty of measurements & significant figures

• ELLE_AW
In summary: So the uncertainty in measuring 1 metre is 1/16" or 0.0625". This is equivalent to 0.001588 m.In summary, the conversion factor of 1m = 39.3701 inches was used to measure a tape with inches to a full meter. The uncertainty in measuring 1 meter using this tape is +/- 0.0625 inches or 0.001588 meters. The last certain digit in the measurement is 1 and the meters should be reported to two significant figures, 1.00.

## Homework Statement

This conversion factor 1m = 39.3701 inches was used, when measuring a tape that had inches on it to a full meter. The measuring tape increased by 0.0625 inch increments, so the 1 meter (39.3701) was estimated to be in between the 39.3125 and 39.3750 on the actual measuring tape.
Based on this what is uncertainty of my measurement in meters? What is the last certain digit? What sig figs would would the meters be reported to accurately (e.g. 1.0 or 1.00) ?

## Homework Equations

conversion factor: 1 m = 39.3701 inches

## The Attempt at a Solution

I think the meter should be written as 1.00

I think the uncertainty would be 0.0625 inches x 1 m / 39.3701 inches = 0.00158 meters

I feel like I"m wrong though.

ELLE_AW said:
when measuring a tape that had inches on it to a full meter.
Not quite sure what this means.
Is the idea that we are trying to measure off a distance of one metre using this tape? If so, we have to choose which of the ##\frac 1{16}##" marks to use.

haruspex said:
Not quite sure what this means.
Is the idea that we are trying to measure off a distance of one metre using this tape? If so, we have to choose which of the ##\frac 1{16}##" marks to use.

Figured it out.

Yes, measuring a distance of 1 meter using this tape that has units of inches. Yes, I just wanted to calculate the uncertainty, but it's basically the smallest increment by which the measuring tool (tape in this case) increases... so +/- 0.0625 inches.

ELLE_AW said:
Figured it out.

Yes, measuring a distance of 1 meter using this tape that has units of inches. Yes, I just wanted to calculate the uncertainty, but it's basically the smallest increment by which the measuring tool (tape in this case) increases... so +/- 0.0625 inches.
I would assume that the tape user is able to select the nearest mark on the tape.

## 1. What is the difference between precision and accuracy in measurements?

Precision refers to the degree of consistency or reproducibility in a measurement, while accuracy refers to how close a measurement is to the true or accepted value. Precision does not necessarily indicate accuracy, as a measurement can be consistently wrong. However, a measurement that is both precise and accurate is considered to be reliable.

## 2. How is uncertainty represented in measurements?

Uncertainty in measurements is typically represented by the number of significant figures. This is the number of digits that are known with certainty, plus one estimated digit. For example, if a measurement is 3.25 cm, the 3 and 2 are known with certainty, while the 5 is an estimated digit. The more significant figures, the more precise the measurement is considered to be.

## 3. How do significant figures affect mathematical operations?

In mathematical operations using measurements, the result should have the same number of significant figures as the measurement with the fewest significant figures. For example, if a measurement is 4.35 cm and another is 1.2 cm, the result of their sum should be rounded to 5.6 cm, as the second measurement only has two significant figures.

## 4. What is the purpose of rounding in significant figures?

Rounding in significant figures helps to maintain the accuracy and precision of a measurement. When a measurement is rounded, it is being expressed to the appropriate degree of uncertainty. This can also help to avoid false precision, where a measurement appears to be more precise than it actually is.

## 5. How is uncertainty of measurements affected by experimental errors?

Uncertainty of measurements can be affected by various types of experimental errors, including random and systematic errors. Random errors are due to chance and can be minimized by taking multiple measurements and calculating an average. Systematic errors are consistent and can be caused by faulty equipment or incorrect procedures. These types of errors can be reduced by using proper calibration and following accurate procedures.