Unit conversion problem

In summary: So, it's either (0.3166667 trucks) x (year) or (1 truck) x (year/(0.3166667 barrels)) = (1 truck/year)(3.155 x 107 barrels).Either way, you must multiply by 1 truck/6000 barrels, and the barrels cancel leaving trucks/year, and the factor 1/6000 must go somewhere in the product.In summary, to find the number of trucks that could run on the oil produced in the US in one year (1.9*10^10 barrels), we can use the conversion factor of 6000 barrels per year per truck. This gives us a result of 3,000,000
  • #1
cytochrome
166
3

Homework Statement


If one truck runs on 6000 barrels of oil per year, how many trucks could run on the oil produced in the US in one year (1.9*10^10 barrels)?

Homework Equations


(6000 barrels/year) used by one truck
(1.9*10^10 barrels/year) for US production

The Attempt at a Solution


I simply divided 1.9*10^10 by 6000 to get 3,000,000.

I'm confused about the fact that 3,000,000 is not in units of "trucks". How can I set up this problem properly to include trucks as my units?
 
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  • #2
Hello cytochrome,

[tex]\left(\frac{1.9 \times 10^{10}~\textrm{barrels}}{1~\textrm{year}}\right) \cdot \left(\frac{1~\textrm{truck}}{6000~\textrm{barrels}}\right)[/tex]

The unit of barrels cancels, leaving trucks and years, so your result is in trucks/year ("trucks per year").

EDIT: ACTUALLY, you can consider the quantity of 6000 to have units of "barrels per truck, per year" which would be barrels/(trucks*years). So, in that case, there would be 1 year in the numerator of the righthand factor in parentheses, and the year unit would cancel as well, leaving only trucks.

However, the way I did it is fine too. In this case, the way to think about it is that a "truck" is a unit of volume equal to the amount of oil needed to run one truck for a year. So, what your unit conversion is doing is saying that the US produces 3,000,000 "trucks" worth of oil per year. It's just a matter of interpretation.
 
Last edited:
  • #3
Another version:

6000 bbl per year per truck

1.9 x 1010 bbl per year
 
  • #4
Chestermiller said:
Another version:

6000 bbl per year per truck

1.9 x 1010 bbl per year

Yup. I had edited my post to include this version (just not LaTeXed).
 
  • #5


To properly set up this problem, you can use dimensional analysis to convert the units to trucks. First, you need to determine the conversion factor between barrels and trucks. This can be calculated by dividing the number of barrels used by one truck (6000 barrels) by the number of trucks (1). This gives a conversion factor of 6000 barrels/truck.

Next, you can set up the problem using this conversion factor:

(1.9*10^10 barrels) x (1 truck/6000 barrels) = 3.167*10^6 trucks

This means that the amount of oil produced in the US in one year (1.9*10^10 barrels) could potentially run 3.167 million trucks for one year. It is important to note that this is just a theoretical calculation and does not take into account other factors such as the efficiency of the trucks or the availability of oil.
 

What is a unit conversion problem?

A unit conversion problem is a mathematical problem that involves converting a quantity from one unit of measurement to another. This is often necessary when working with different systems of measurement, such as converting from metric units to imperial units.

Why is unit conversion important in science?

Unit conversion is important in science because it allows researchers to communicate and compare their findings using a common system of measurement. It also allows for easier interpretation of data, as different units of measurement may have different scales and values.

What are the common units of measurement used in unit conversion problems?

The most commonly used units of measurement in unit conversion problems include length (meters, centimeters, inches), mass (grams, kilograms, pounds), volume (liters, milliliters, gallons), and time (seconds, minutes, hours).

What are some tips for solving unit conversion problems?

Some tips for solving unit conversion problems include setting up a conversion factor using the given units and the desired units, canceling out units using dimensional analysis, and double-checking the final answer to ensure it has the correct units.

Are there any common mistakes to avoid when solving unit conversion problems?

Yes, some common mistakes to avoid when solving unit conversion problems include using incorrect conversion factors, not cancelling out units correctly, and forgetting to include the units in the final answer. It is also important to pay attention to the direction of the conversion (e.g. converting from meters to feet vs feet to meters).

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