Question

Merchants usually sell small nuts, washers, and bolts by weight (like jelly beans!) rather than by individually counting the items. Suppose a particular type of washer weighs \(0.110 \mathrm{~g}\) on the average. What would 100 such washers weigh? How many washers would there be in \(100 . \mathrm{g}\) of washers?

Short answer

The total weight of 100 washers is 11 grams, and there would be approximately 909 washers in 100 grams of washers.

Step-by-step solution

Part 1: Finding the weight of 100 washers

First, we are given the average weight of one washer, which is 0.110 g. To find the total weight of 100 washers, we simply need to multiply the individual weight by the number of washers. Total weight = Individual weight × Number of washers = \(0.110 \mathrm{~g}\) × \(100\) = \(11 \mathrm{~g}\) So, the total weight of 100 washers is 11 grams.

Part 2: Find the number of washers in 100 grams

Now, we are given a total weight of 100 grams and asked to find out how many washers are present in that weight. To calculate this, we will divide the total weight by the weight of one individual washer. Number of washers = Total weight ÷ Individual weight = \(100 \mathrm{~g}\) ÷ \(0.110 \mathrm{~g}\) ≈ \(909.1\) Since we cannot have a fraction of a washer, we round down to 909 washers. Therefore, there would be approximately 909 washers in 100 grams of washers.

Key concepts

Understanding Average Weight

The concept of average weight is fundamental when dealing with bulk items such as washers, nuts, and bolts. Average weight is the typical weight of an item when individual weights vary slightly. Imagine you have numerous washers, each weighing around 0.110 grams. Some might weigh slightly more, and some less. However, 0.110 grams is considered the average weight.
An average weight allows you to perform calculations without needing to weigh each item.
To find the total weight of multiple items, you simply multiply the average weight by the number of items. In a practical situation where you have 100 washers, the calculation would look like:

• Average weight of one washer = 0.110 grams
• Number of washers = 100
• Total weight = 0.110 grams × 100 = 11 grams

So, 100 washers would weigh a total of 11 grams, assuming each washer is close to the average.

The Importance of Unit Conversion

Unit conversion is essential in many areas of math and science, helping ensure consistency and accuracy. For weight measurements, it's important to stay consistent with the unit type, whether it's grams, kilograms, ounces, or pounds.
In the context of this problem, we're dealing with weights in grams. This exercise doesn't require conversion because all given information uses the same units. However, knowing how to convert units is useful. For example, if the problem changed or required expressing weight in kilograms, remember that:

• 1 kilogram (kg) = 1000 grams (g)
• Therefore, 11 grams = 0.011 kilograms

Mastering unit conversion ensures precise calculations and allows flexibility in interpreting information given in various units.

Rounding in Calculations

Rounding is crucial when dealing with situations that don't accommodate fractions, such as counting discrete items like washers. When you calculate the number of washers in a total weight and the result is not a whole number, you must round. Consider a calculation where 100 grams are divided by 0.110 grams per washer:

• The raw result is approximately 909.1 washers

Since you cannot have part of a washer, you must apply rounding rules. In most practical applications, especially involving tangible items, you would round down to the nearest whole number.
Thus, you would have 909 washers. Rounding helps align calculations with real-world constraints and ensures outcomes are practical and actionable.