-5.47 and 5.47 on a number line are not equal to \(|-5.47|\).

Explain the error.

The absolute value of -5.47 (which is |-5.47|) is always a positive number so the absolute value of -5.47 equals 5.47

Answered by rj6thstreet | 2024-06-10

The student's error lies in the misunderstanding of the absolute value function and its representation on a number line. The absolute value of a number is the distance from that number to zero on the number line, regardless of direction. Therefore, the absolute value of -5.47 is 5.47, which means that |-5.47| equals 5.47, not -5.47.
When considering the numbers -5.47 and 5.47 on a number line, they are equal in magnitude but opposite in sign. The absolute value of a negative number, such as -5.47, is positive, and this common error usually stems from not applying the absolute value operation correctly.
An example to illustrate this is as follows: The absolute value of -6 is 6 because on the number line, -6 is 6 units away from zero. Similarly, |-5.47| is 5.47.

Answered by JoanBlondell | 2024-06-24

The student's error stems from a misunderstanding of absolute value; |-5.47| equals 5.47, which is not equal to -5.47. Absolute values measure distance and are always non-negative. Therefore, -5.47 and 5.47 are not equal, but |-5.47| equals 5.47, highlighting the difference between the two concepts.
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Answered by JoanBlondell | 2024-10-10