High School

Use the rules of significant figures to report the answer to this math question:

(454.3 cL × 17.84 dL / 3.1 L = ?)

(Hint: Be sure to convert all measurements to the same units)

Select one:

A. 2.6 L
B. 2.6144 L
C. 2.6 × 10^2 L
D. 2.6144 × 10^2 L

Answer :

Final answer:

After converting all units to liters and performing the calculation, the volume is found to be approximately 2.6145 L. However, based on the rule of significant figures, and the minimum number of significant figures (two) given amongst the values used in the calculation, the answer is rounded to 2.6 L.

Explanation:

To solve for the volume in liters given the formula (454.3 cL x 17.84 dl / 3.1 L), we must begin by converting all measurements to the same unit. Since we want our answer in liters, let's convert centiliters (cL) and deciliters (dl) to liters. There are 100 cL in a liter and 10 dl in a liter. Thus, we have:

454.3 cL = 454.3 / 100 L = 4.543 L
17.84 dl = 17.84 / 10 L = 1.784 L

Now, we can perform the calculation in liters:

(4.543 L x 1.784 L) / 3.1 L = 8.105952 L / 3.1 L ≈ 2.6145 L

Following the rules of significant figures, since the smallest number of significant figures in the given measurements is two (3.1 L), our answer should also be rounded to two significant figures. Therefore, we round 2.6145 L to 2.6 L.

The correct choice is option a. 2.6 L, when considering significant figures rules.

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