In contrast to identical measurements of the same quantity, if you combine (add,

Question

In contrast to identical measurements of the same quantity, if you combine (add, subtract, multiply, or divide) measurements of two different quantities, each of which has an associated uncertainty, the uncertainty in the combined measurement is larger than the individual uncertainties. As an example, let's say I am getting hay delivered for my goats. The hay delivery man was in a hurry, so doesn't remember exactly how many bales he put on his truck: he says it's somewhere between 20 and 30 bales. How would you express the number of bales and its uncertainty? Write both numbers as whole numbers.

My anwser: 25 -/+5

Let's say that the hay delivery man unloads the bales onto my driveway in a big stack, so that they are hard to count. I start moving them one at a time into the goat pen, but it's hot and I get sort of bored, so lose track of how many I've moved. I know it's at least 8, but it could be as many as 12.Write down the number of bales I've moved and its uncertainty. Both numbers should be whole numbers, written in digits rather than words.

My answer: 10 -/+2

Now I'm wondering how many bales I have left to move. Given the range of bales possibly delivered, and the range of bales I've possibly moved, what is the range of bales that are remaining?

Write down the minimum number of bales in the left box and the maximum number in the right box. Both numbers should be whole numbers, written in digits rather than words.

______ -/+______

Explanation / Answer

We know that the uncertainity associated with any measurement increases when we do any mathematical operation over some quantities which have some sort of uncertainity in their measurement and hence we can see from the first two conditions that there are uncertainties associated with them , hence the final uncertainity is equal to:

The value of measurement will be: 25 - 10 = 15

The uncertainity is: (-/+5) + (-/+2) = -/+7

Therefore, minimum number of bales in the left box and the maximum number in the right box can be represented as 15 -/+7.

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