Comparing Absolute Values: Are |56| and |-5.6| Opposite Numbers?

Are the numbers opposite?

$\left|56\right|,\left|-5.6\right|$

To solve this problem, we shall first evaluate the absolute value of each given number.

• Step 1: Calculate $\left|56\right|$. Since the absolute value of a number is its distance from zero on the number line without regard to sign, $\left|56\right| = 56$.

• Step 2: Calculate $\left|-5.6\right|$. Similarly, $\left|-5.6\right|$ is the magnitude of $-5.6$, hence $\left|-5.6\right| = 5.6$.

Now that we have evaluated the absolute values:

• $\left|56\right| = 56$
• $\left|-5.6\right| = 5.6$

We compare the obtained results to check if they are opposites. By definition, opposites are numbers that are equal in magnitude but different in sign. However, since absolute values are always non-negative, the idea of "opposites" does not apply directly to absolute values. In this context, we check if their magnitudes are the same.

Clearly, $56$ is not equal to $5.6$. Therefore, the numbers $\left|56\right|$ and $\left|-5.6\right|$ are not opposites.

The correct answer is No.