I'm kind of having difficulty with a question involving dimensional analysis. I'm confused how I would convert some units into others and what to divide. Here's the question.
One 5lb Hershey's kiss is equivalent to how many little Hershey's Kisses?
(1 Hershey Kiss is equal to 4.09 grams)
Fist, you want to convert 5 lb candy to grams. We know 1 lb = 454 grams. We can write the conversion factor as 1 lb/454 g OR we can write it as 454 g/1 lb. How do we know which factor to use (which may be your problem). Here is how to do it.
5 lb Hershey x (factor) = ?? grams Hershey
Let's try either of the factors.
5 lb Hershey x (l lb/454 g) = ?? you can do the math, BUT we don't need to do it. We look at the units and we will know if we picked the right factor. Notice we have lb x lb in the numerator and grams in the denominator so the units for ?? answer are ?? lb2/grams. Is that what we want? NO. So we pick the other one.
5 lb Hershey x (454 g/1 lb) = 2,270 grams. You notice the lb unit cancels which leaves the grams unit (which is what we want). You need not go through a hit and miss procedure each time you want to make a conversion. Just remember the unit we DON'T want to keep is to cancel (whether it's in the numerator or denominator) and the unit we want to keep is left.(If the unit we want to lose is in the numerator we make the factor with that unit in the denominator; if the unit we want to lose is in the denominator, we make the factor with that unit in the numerator.) The second part of the problem is to calculate how many "kisses" are in the 2,270 grams. Factors are 1 kiss = 4.09 grams and 4.09 grams = 1 kiss.
2,270 grams x (factor) = # kisses.
2,270g x (1 kiss/4.09g) = 555. Again, note that the gram unit cancels and the kiss unit is left so the answer is 555 kisses.
Thank you. I had quite a bit a trouble with this and appreciate the quick response.
To convert units using dimensional analysis, you need to use conversion factors. Conversion factors allow you to cancel out units and only keep the desired units in the final answer. Here's how you can solve the given question step-by-step:
Step 1: Identify the given information:
- 1 Hershey's Kiss is equal to 4.09 grams
- You want to find how many little Hershey's Kisses are equivalent to 5 pounds.
Step 2: Set up the conversion factors:
Conversion factor 1: 1 Hershey's Kiss = 4.09 grams
Conversion factor 2: 1 pound = 453.592 grams
Step 3: Convert pounds to grams:
Multiply 5 pounds by the conversion factor of 453.592 grams per 1 pound. This will give you the weight of 5 pounds in grams.
5 pounds * (453.592 grams / 1 pound) = 2267.96 grams
Step 4: Set up the final conversion:
Now that you have the weight in grams (2267.96 grams), you can set up the final conversion to find the number of little Hershey's Kisses.
2267.96 grams * (1 Hershey's Kiss / 4.09 grams) = 554.06 Hershey's Kisses
Step 5: Round your answer:
Since you can't have a fraction of a Hershey's Kiss, round your answer to the nearest whole number.
Final Answer: One 5-pound Hershey's Kiss is equivalent to approximately 554 little Hershey's Kisses.