This question illustrates the potential consequences of using rounded numerical results prematurely. Maintain sufficient digits in intermediate calculations to ensure the final answer is precise. Consider the following problem: You wish to purchase 100 pens. One store offers a 10% discount on pens priced at $4.99 each, while another provides a 15% discount on pens costing $5.34 each. (a) What is the price per pen at the first store after the discount? (b) What is the price per pen at the second store after the discount? (c) What is the total price difference for 100 pens between the two stores?

(a) To calculate the price per pen at the first store after a 10% discount on pens priced at $4.99, we first need to determine how much the discount is in dollars. To do this, we take 10% of $4.99:

Discount = 10% of $4.99 = 0.10 * $4.99 = $0.499

Since we usually don't deal with fractions of a cent, we should round the discount to the nearest cent, which results in:

Discount = $0.50 (after rounding)

Now, to find the price per pen after the discount, we subtract the discount from the original price:

Price per pen = Original price - Discount = $4.99 - $0.50 = $4.49

So, the price per pen at the first store after the discount is $4.49.

(b) For the second store, which offers a 15% discount on pens costing $5.34 each, we perform a similar calculation:

Discount = 15% of $5.34 = 0.15 * $5.34 = $0.801

Again, rounding to the nearest cent:

Discount = $0.80 (after rounding)

Now, we find the discounted price per pen at the second store:

Price per pen = Original price - Discount = $5.34 - $0.80 = $4.54

So, the price per pen at the second store after the discount is $4.54.

(c) To find out the total price difference for 100 pens between the two stores, we can calculate the total price at each store and then subtract them.

Total price at the first store for 100 pens:

Total price = 100 * Price per pen at the first store Total price = 100 * $4.49 Total price = $449

Total price at the second store for 100 pens:

Total price = 100 * Price per pen at the second store Total price = 100 * $4.54 Total price = $454

Finally, the total price difference:

Price difference = Total price at the second store - Total price at the first store Price difference = $454 - $449 Price difference = $5

So, the total price difference for 100 pens between the two stores is $5, in favor of the first store.

Extra: When dealing with discounts, percentages play a crucial role. A percentage discount off a product means you pay that percentage less than the full price. To calculate a percent of a number, you multiply the original number by the percentage expressed as a decimal. This is why we converted 10% to 0.10 and 15% to 0.15 in the calculations above.

When you're calculating totals or discounts, it's important to keep enough digits in your intermediate values so that the final answer is accurate. Rounding too soon can result in incorrect totals, which can be significant when dealing with larger quantities or money.

Moreover, when comparing discounts, it's beneficial to look at the actual cost instead of just the discount percentages, as shown in this example. A higher discount percentage doesn't necessarily translate to a lower cost if the original prices are different. This is a valuable lesson in practical arithmetic and financial literacy for both students and consumers.