Question

State the absolute value and the opposite of the number.

$-78$

Short answer

The absolute value is78, and the opposite of the number is78.

Step-by-step solution

Step-1 – Absolute value of a number

Absolute value of any positive or negative number is always positive and equal to the magnitude of the number. The absolute value of a number N is denoted by $\left|N\right|$.

For example, the absolute value of 3 is denoted by $\left|3\right|$and is equal to 3.

And the absolute value of $-4$is denoted by $\left|-4\right|$and is equal to 4.

Step-2 – Opposite of a number

Opposite of any real number can be obtained by multiplying it with $-1$. On the number line, opposite of any number be located on the opposite side at the same distance from the midpoint 0.

For example, the opposite of the number $-5$ is 5.

Step-3 – Evaluate the absolute value

The number $-78$ is at a distance of 78 units to the left of 0 on the number line.

So, the absolute value of the given number $-78$ is given by

$\left|-78\right|=78$

Thus, the absolute value of the given number is 78.

Step-4 – Find the opposite of the number

In order to find the opposite of the number, multiply it with $-1$.

So, the opposite of the given number is

$-1\left(-78\right)=78$

Thus, the opposite of the number is $78$.