What is the meaning of a measurement expressed as 2.0 cm -/+ 0.05 cm?

AI Thread Summary
The expression 2.0 cm -/+ 0.05 cm indicates that the true measurement can vary within a range due to uncertainty. Specifically, this means the actual value lies between 1.95 cm and 2.05 cm. The discussion clarifies that the +/- notation represents the measurement's error margin, not a broader range. It emphasizes the importance of understanding statistical interpretation, suggesting a 68% probability that the true value falls within this range. Accurate interpretation of such measurements is crucial in scientific and technical contexts.
Quarlep
Messages
257
Reaction score
4
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm
 
Mathematics news on Phys.org
Quarlep said:
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm

It means the error is between the value written after -/+, so for example 1.0 km -/+ 0.5 km. That means we are not certain that the measurement is 1.0 km as given by whatever instruments we have. The real value can range between 1.5 km and 0.5 km.
 
Quarlep said:
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm

Your first thought ("between") is right, but have you dropped a decimal place in there? ##2.0{\pm}0.05## means between 1.95 and 2.05, not 1.5 and 2.5
 
I think of the +/- as the uncertainty in the measurement in a statistical sense. This may be a subtlety different view to that posted above. I don't interpret those bounds as definitely encompassing the 'true measurement'. Usually I'd take it to mean that there's a 68% chance (1 sigma) that the true measurement is in that range, assuming 'normal' statistics of course. Just my view, others may disagree!
 
Quarlep said:
Hi I saw something in Wikipedia and I am confused. I saw something like this
2.0 cm -/+ 0.05 cm Whats that mean?
My first opinion Between 1,5 and 2,5
My second opinion 1,5 cm or 2,5 cm

Seydlitz said:
It means the error is between the value written after -/+, so for example 1.0 km -/+ 0.5 km. That means we are not certain that the measurement is 1.0 km as given by whatever instruments we have. The real value can range between 1.5 km and 0.5 km.
As Nugatory points out, the error portion is ##\pm## 0.05. Also, the units involved are centimeters, not kilometers

Nugatory said:
Your first thought ("between") is right, but have you dropped a decimal place in there? ##2.0{\pm}0.05## means between 1.95 and 2.05, not 1.5 and 2.5
Quarlep, the measurement is between 1.95 cm and 2.05 cm.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top