The propagation errors we can find the uncertainty of a given magnitude is the sum of the uncertainties of each magnitude.
Δm = ∑
Physical quantities are precise values of a variable, but all measurements have an uncertainty, in the case of direct measurements the uncertainty is equal to the precision of the given instrument.
When you have derived variables, that is, when measurements are made with different instruments, each with a different uncertainty, the way to find the uncertainty or error is used the propagation errors to use the variation of each parameter, keeping the others constant and taking the worst of the cases, all the errors add up.
If m is the calculated quantity, x_i the measured values and Δx_i the uncertainty of each value, the total uncertainty is
Δm = ∑
| dm / dx_i | Dx_i
for instance:
If the magnitude is a average of two magnitudes measured each with a different error
m =
Δm = |
| Δx₁ + |
| Δx₂
= ½
= ½
Δm =
Δx₁ + ½ Δx₂
Δm = Δx₁ + Δx₂
In conclusion, using the propagation errors we can find the uncertainty of a given quantity is the sum of the uncertainties of each measured quantity.
Learn more about propagation errors here:
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Answer:
Archaeologist use radioactive isotopes to determine the ages of various objects, rocks and materials. This is called radioactive dating. Radioactive isotope Carbon-14 is widely used for this dating process.
Scientists use radioactive isotopes in agriculture to monitor or study the uptake and use of essential nutrients by plants from the soil. This helps to determine viability, productivity and nutritious ability of the plants on a piece of land.
Geologists use radioactive isotopes to trace leaks in underground water storage, pipes. Radioactive isotopes are effective tracers because their radioactivity can be easily detected.
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