Since measurements are uncertain any calculation that involves a measurement will yield results that are uncertain. To see how this works calculate the minimum and maximum possible values you can get from the calculation below, where [ _ , _ ] represents the [minimum, maximum] values of the uncertain number.

3.56 - [1.17, 1.19] =?

The minimum value is:

The maximum value is:

Question

Since measurements are uncertain any calculation that involves a measurement will yield results that are uncertain. To see how this works calculate the minimum and maximum possible values you can get from the calculation below, where [ _ , _ ] represents the [minimum, maximum] values of the uncertain number.

3.56 - [1.17, 1.19] =?

The minimum value is:
 
 The maximum value is:

BlackTom AI · Accepted Answer

Question restatement: You are asked to find the minimum and maximum possible values of the expression 3.56 - [1.17, 1.19], where the brackets denote an uncertain quantity with a range from 1.17 to 1.19.

First, recall how subtraction with an uncertain value works: to get the smallest possible result, subtract the largest possible value from the fixed number. To get the largest possible result, subtract the smallest possible value from the fixed number.

Step 1 — Compute the minimum value: subtract the maximum of the range (1.19) from 3.56.
- 3.56 - 1.19 = 2.37
- Therefore, the minimum value of the expression is 2.37.

Step 2 — Compute the maximum value: subtract the minimum of the range (1.17) from 3.56.
- 3.56 - 1.17 = 2.39
- Therefore, the maximum value of the expression is 2.39.

Summary of results: the range of possible values for 3.56 - [1.17, 1.19] is [2.37, 2.39]. The two blanks should be filled with 2.37 for the minimum and 2.39 for the maximum.

If you think about it intuitively, increasing the subtracted value (moving from 1.17 to 1.19) decreases the result, hence the minimum occurs at 1.19 and the maximum occurs at 1.17. This aligns with performing the two boundary calculations shown above.

CHEM 105-A09C Prelab 3 Measurements, Significant Digits & Density

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