Question

Which of the following numbers is greatest?

• A. -0.225
• B. -0.0225
• C. -0.323
• D. -0.0325
• E. -0.3205

Hint:

Visualize a number line. Numbers increase as you move from left to right. For negative numbers, numbers closer to zero (e.g., -1) are greater than numbers further from zero (e.g., -10).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question asks to identify the greatest number from a list of negative decimal numbers. For negative numbers, the "greatest" number is the one that is least negative, meaning it is closest to 0 on the number line.
Step 2: Key Formula or Approach:
To find the greatest negative number, we can compare the absolute values of the numbers. The negative number with the smallest absolute value is the greatest.
Step 3: Detailed Explanation:
We have the following numbers: -0.225, -0.0225, -0.323, -0.0325, and -0.3205.
Let's find their absolute values:
(A) \(|-0.225| = 0.225\)
(B) \(|-0.0225| = 0.0225\)
(C) \(|-0.323| = 0.323\)
(D) \(|-0.0325| = 0.0325\)
(E) \(|-0.3205| = 0.3205\)
Now, we compare these positive decimal values to find the smallest one.
- Comparing 0.0225 and 0.0325, we see that 0.0225 is smaller.
- Comparing 0.0225 with the rest (0.225, 0.323, 0.3205), it is clearly the smallest because its first non-zero digit is in the hundredths place, while for the others it's in the tenths place (or in the case of 0.0325, the value in the hundredths place is larger).
The smallest absolute value is 0.0225.
Step 4: Final Answer:
The number with the smallest absolute value is -0.0225. Therefore, -0.0225 is the greatest number in the list.