Compare the absolute values of the following numbers using the symbols >, <, or =: 1. |-4.67| and |3| 2. |-15| and |15|
Understand the Problem
The question asks to compare two numbers using the symbols >, <, or =. The first question compares the absolute value of -4.67 and 3. The second question compares the absolute value of -15 and 15.
Answer
1. $|-4.67| > |3|$ 2. $|-15| = |15|$
Answer for screen readers
- $|-4.67| > |3|$
- $|-15| = |15|$
Steps to Solve
- Evaluate the absolute value of -4.67
The absolute value of a number is its distance from 0 on the number line. The absolute value of -4.67, denoted as $|-4.67|$, is 4.67. $$ |-4.67| = 4.67 $$
- Compare 4.67 with 3
Since 4.67 is greater than 3, we use the ">" symbol. $$ 4.67 > 3 $$
- Evaluate the absolute value of -15 and 15
The absolute value of -15 is 15, denoted as $|-15|$, is 15. The absolute value of 15, denoted as $|15|$, is 15. $$ |-15| = 15 $$ $$ |15| = 15 $$
- Compare 15 with 15
Since 15 is equal to 15, we use the "=" symbol. $$ 15 = 15 $$
- $|-4.67| > |3|$
- $|-15| = |15|$
More Information
The absolute value represents the distance from zero. Therefore, it is always non-negative.
Tips
A common mistake is to think that the absolute value of a negative number is negative. Remember, absolute value is distance, and distance is always non-negative.
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