Uncertainty of measurements & significant figures

Click For Summary
SUMMARY

The discussion focuses on calculating the uncertainty of measurements when converting from inches to meters using the conversion factor of 1 m = 39.3701 inches. The measurement uncertainty is determined to be +/- 0.0625 inches, which translates to an uncertainty of 0.00158 meters. The final measurement of 1 meter should be reported as 1.00 meters, reflecting the precision of the measuring tape increments.

PREREQUISITES
  • Understanding of significant figures and their application in measurements
  • Knowledge of unit conversion, specifically from inches to meters
  • Familiarity with the concept of measurement uncertainty
  • Basic arithmetic operations involving decimals and fractions
NEXT STEPS
  • Study the principles of significant figures in scientific measurements
  • Learn about measurement uncertainty and how to calculate it in various contexts
  • Explore unit conversion techniques, particularly between imperial and metric systems
  • Investigate the impact of measuring tool precision on reported measurements
USEFUL FOR

Students in physics or engineering, educators teaching measurement concepts, and professionals involved in quality control or precision measurement tasks.

ELLE_AW
Messages
16
Reaction score
0

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.
 
Physics news on Phys.org
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.
 

Similar threads

Replies
9
Views
3K
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
753
  • · Replies 2 ·
Replies
2
Views
662
  • · Replies 11 ·
Replies
11
Views
2K