Uncertainty of measurements & significant figures

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Homework Help Overview

The discussion revolves around measuring a distance of one meter using a tape measure that displays inches, specifically focusing on the conversion factor between meters and inches. Participants are exploring the concepts of uncertainty in measurements and the appropriate number of significant figures to report the measurement in meters.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the method of measuring one meter using a tape with inch increments and question how to determine the uncertainty based on the smallest increment of the tape. There is also a consideration of how to report the measurement in terms of significant figures.

Discussion Status

Some participants have clarified their understanding of the measurement process and the uncertainty involved. There is an acknowledgment of the smallest increment of the measuring tool, and discussions are ongoing regarding how to accurately report the measurement.

Contextual Notes

Participants are considering the implications of the measuring tape's increments and how they affect the reported uncertainty and significant figures. The original poster expresses uncertainty about their calculations and assumptions regarding the measurement process.

ELLE_AW
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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.
 
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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.
 

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