Craig G. answered • 02/19/20
Veteran teacher/tutor in Algebra, Chemistry, French & Calculus
Unit conversions are essential for all math and science courses beyond Algebra I, especially chemistry and physics where new units (e.g., moles, Joules, Newtons, etc. are learned each chapter/module of study). Always, start with your given quantity(ies) and set them up so that units cancel. A unit in the numerator and the same unit in the denominator “cancel” because anything divided by itself is 1. For example, g divided by g = 1. Finally, before starting, you will need to know what conversions your teacher is requiring you to memorize. For this problem, it looks like the 5 conversions noted at the bottom of your problem.
To get started, I’ll do the first few steps. (Notice the question that I ask at the end of each step.)
[1] (55 mi/h) * (3.0 h) = 165 (mi*h/h) .... [The h on top cancels with the h on bottom] = 165 mi. Do we have the correct unit in our answer? (No, we have miles, and we were asked to find gallons.)
[2 - Done incorrectly on purpose here] (165 mi) * (8.0 mi / L) = 1320 mi*mi/L [Both mi are in the numerator. These do not cancel. Multiplication was not the correct operator. To get the miles to cancel, we must divide. To get L in the numerator, we will set it up like {2b}.
{2b - Correctly done} (165 mi) / (8.0 mi / L) = 20.625 mi*L / mi = 20.625 L because the mi cancel. Do we have the correct unit in our answer? (No, we have L and were asked to find gallons.)
[3] We are needing to convert L to gallons. I have my students memorize this number, but your teacher has given other facts to memorize. How do we get from L to gal? Looking at your options, you have 1 L = 1.057 qt. From our last answer, we have liters in the numerator, so we need to set up the conversion with L in the denominator
(20.625 L) * (1.057 qt / 1 L) = 21.8006 qt. Do we have the correct unit in our answer? (No, we have qt and were asked to find gallons.)
[4] Do you see a conversion between qt and gallons in your list? Keep going until your answer to the bolded question is yes.
[5] Significant digits/figures is a completely different skill. This problem only used multiplication and division, so look at the original numbers that were given [55, 8, and 3.0]. Those have 2 sig figs, 1 sig fig, and 2 sig figs. The smallest of those is “1,” so your final answer will only have 1 significant figure.
Note: If the original problem said 8.0 mi/L, then all of the given values would have 2 sig figs, and your final answer would also need 2 significant figures.
