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Chapter 24: Problem 2

Which one of the following products has the greatest value? (A) \(6.00 \times 0.20\) (B) \(6.01 \times 0.19\) (C) \(6.02 \times 0.18\) (D) \(6.03 \times 0.17\) (E) \(\quad 6.04 \times 0.16\)

Short Answer

Expert verified
The greatest value is from Option (A): 1.20.

Step by step solution

01

Understanding the Problem

We need to determine which of the given products has the greatest numerical value. The options are products of two numbers, and our task is to calculate each product and compare them.
02

Calculating Option A

For Option (A), calculate the product: \(6.00 \times 0.20 = 1.20\).
03

Calculating Option B

For Option (B), calculate the product: \(6.01 \times 0.19 = 1.1419\).
04

Calculating Option C

For Option (C), calculate the product: \(6.02 \times 0.18 = 1.0836\).
05

Calculating Option D

For Option (D), calculate the product: \(6.03 \times 0.17 = 1.0251\).
06

Calculating Option E

For Option (E), calculate the product: \(6.04 \times 0.16 = 0.9664\).
07

Comparing the Products

We compare the calculated values: 1.20 (A), 1.1419 (B), 1.0836 (C), 1.0251 (D), 0.9664 (E). The greatest value is 1.20 from Option (A).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication
Multiplication is one of the fundamental arithmetic operations that involves combining equal groups to find a total amount. In this exercise, we're dealing with decimal multiplication, which can sometimes seem complex, but is straightforward once you understand the process.
When multiplying decimals, it's essential to note:
  • Each digit in numbers maintains its value per its place (ones, tenths, hundredths, etc.).
  • After multiplying, count all the decimal places in both numbers being multiplied to accurately place the decimal in the answer.
For example, multiplying 6.00 and 0.20 involves multiplying as if they were 600 and 20. Once you calculate the product as 12000, you count three decimal places starting from the right, resulting in 1.200, which simplifies to 1.20.
Numerical Comparison
Numerical comparison is a critical skill, especially when determining which number in a set is the largest, smallest, or fits particular criteria. In this problem, you're comparing the products obtained from multiplying two numbers in each option.
Here are steps to effectively compare numbers:
  • Line up the numbers at the decimal point for clarity.
  • Compare digit by digit starting from the left, where numbers have greater value (i.e., higher left-digit means larger number).
  • If numbers are close, keep your comparison precise to avoid mistakes, especially in multiple-step math problems.
In the given options, starting comparison of the values 1.20, 1.1419, 1.0836, 1.0251, and 0.9664 confirms that 1.20 is the greatest since its whole number part ("1.") outmatches the others right from the start.
Arithmetic Calculations
Performing arithmetic calculations involves executing several steps, especially when dealing with both integers and decimals. In the context of this problem, arithmetic calculations refer to the act of accurately computing products.
When doing these calculations, remember:
  • Break down calculations into smaller, manageable parts.
  • Use a calculator for precision, especially with decimal multiplication.
  • Re-do calculations if results seem off, ensuring the operations align with logical expectations.
This exercise required calculating five distinct products, each involving decimals, to determine the highest. A crucial strategy is to do each step methodically and compare results incrementally, which was vital in identifying that Option (A) resulted in the highest value at 1.20.

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Most popular questions from this chapter

There are 5 packers \(A, B, C, D\), and \(E\) in a company. The five packers \(A, B, C, D\) and \(E\) charge \(\$ 66\), \(\$ 52\), \(\$ 46, \$ 32\), and \(\$ 28\), respectively, to pack each item. The time taken by the packers to pack one item is 20 minutes, 24 minutes, 30 minutes, 40 minutes and 48 minutes, respectively. All the items are sold at the end of the day. Each item earns a profit of 100 dollars, and the packers are paid from this profit. If each packer works 8 hours a day, which packer contributes the most to the net profit of the company? (A) Packer \(A\) (B) Packer \(B\) (C) Packer \(C\) (D) Packer \(D\) (E) Packer \(E\)

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