Problem 82 - Chemistry Matter and Change

Question

Popcorn The average mass of a kernel of popcorn is 0.125 g. If 1 pound \(=16\) ounces, and 1 ounce \(=28.3 \mathrm{g},\) then how many kernels of popcorn are there in 0.500 pounds of popcorn?

Step-by-Step Solution

Answer

There are 1811 kernels of popcorn in 0.500 pounds.

Step 1: Convert pounds to grams

First, we need to convert 0.500 pounds of popcorn to grams. Since 1 pound is equal to 16 ounces, we calculate the number of ounces in 0.500 pounds by multiplying 0.500 by 16, which gives us 8 ounces. Next, we convert ounces to grams: since 1 ounce equals 28.3 grams, we multiply 8 by 28.3, resulting in 226.4 grams of popcorn.

Step 2: Determine the number of kernels

Now that we have the total mass of popcorn in grams as 226.4 grams, we need to find out how many kernels this represents. Given that each kernel has an average mass of 0.125 grams, we divide the total mass by the mass of one kernel: \( \frac{226.4}{0.125} = 1811.2 \). Since we can't have a fraction of a kernel, we round down to 1811 kernels.

Key Concepts

Unit Conversion

Unit conversion is a critical skill in mathematics and science, allowing us to switch between different measurements easily. When converting units, it's important to know the conversion factors.

In this exercise, you're converting from pounds to ounces and then to grams. Here's a quick overview:

• First, you convert pounds to ounces. Knowing that 1 pound equals 16 ounces helps. To convert, simply multiply the number of pounds by 16. For example, 0.500 pounds is equivalent to 0.500 x 16 = 8 ounces.


• Next, convert ounces to grams. Here, you use the conversion factor that 1 ounce equals 28.3 grams. So, multiply the ounces by 28.3 to find out grams. When you have 8 ounces, multiply by 28.3 to get 226.4 grams.

These steps show the importance of understanding and applying conversion factors to create a bridge between different units of measurement.

Mass Calculation

Mass calculation involves determining the amount of matter in an object, usually measured in grams or kilograms.
In this context, it's all about finding out how many kernels of popcorn add up to a certain mass.

Once you've converted the weight of popcorn from pounds to grams, which is 226.4 grams in our example, you calculate how many individual kernels that mass represents. You do this by dividing the total mass by the mass of one kernel. Here, the mass of one kernel is 0.125 grams.

• Perform the division: 226.4 grams (total mass) / 0.125 grams (mass per kernel) = 1811.2 kernels.
• This calculation shows how the total mass can be split into smaller, easily countable units, which are the kernels in this exercise.

Mass calculation gives you a sense of how small units combine to form a total mass, which is particularly useful in converting bulk ingredients into individual pieces.

Mathematical Rounding

Mathematical rounding is the process of adjusting numbers to make them simpler or fit a particular purpose, typically for convenience.
Understanding rounding is essential when dealing with items that cannot be divided further into fractions in practical scenarios, like kernels in our popcorn example.

• After calculating you have 1811.2 kernels, you need to round because you can't have a fraction of a kernel.
• In most real-world applications, rounding is handled by removing the decimal. When rounding 1811.2, you get 1811 kernels.
• A general rule is to round down when you have a situation where a fraction of a unit is unusable or impractical, which is applicable here since you can't use a part of a popcorn kernel.

This simple concept of rounding can have significant effects on calculations and is vital in ensuring accuracy in many practical situations.