Question Video: Finding the Uncertainty in a Given Quantity Squared | Nagwa Question Video: Finding the Uncertainty in a Given Quantity Squared | Nagwa

# Question Video: Finding the Uncertainty in a Given Quantity Squared Physics • First Year of Secondary School

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In an experiment, a quantity π₯ is found to have a value of 4 Β± 0.1. What is the uncertainty in π₯Β²?

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### Video Transcript

In an experiment, a quantity π₯ is found to have a value of four plus or minus 0.1. What is the uncertainty in π₯ squared?

Weβre told that the value of this quantity π₯ is four plus or minus 0.1. This number 0.1 is considered the uncertainty in π₯. Our question asks us to solve for the uncertainty in π₯ squared. If we write out π₯ times π₯, it would look like this. We can see that π₯ squared is equal to four times four, or 16. But thereβs also an uncertainty associated with this result.

To find out what that is, letβs note that, in general, if we have two numbers β weβll call them π and π β with associated uncertainties π π and π π and if a third number π is equal to the product of π and π, then the uncertainty in that product β weβll call it π π β is equal to π times the uncertainty of π plus π times the uncertainty of π. When we consider multiplying π₯ by itself, we could think of the first four here as π and the first 0.1 as the uncertainty in π and then the second four as π and the second 0.1 as π sub π.

According to our equation then, the uncertainty in π₯ squared is π β thatβs four β times π sub π, thatβs 0.1, plus π β thatβs also four β times π sub π, 0.1. Four times 0.1 is equal to 0.4. And if we add 0.4 to 0.4, we get 0.8. This is the overall uncertainty in our product π₯ squared.

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