# Whats the absolute value of abs(11-pi)?

Aug 2, 2015

7.87

#### Explanation:

Since $\pi$ equals 3.14, 11-3.14 would be 7.87

Aug 2, 2015

$\left\mid 11 - \pi \right\mid = 11 - \pi$

#### Explanation:

For every possible real $u$,

$\left\mid u \right\mid = \left\{\begin{matrix}u & \text{if" & u >= 0 \\ -u & "if} & u < 0\end{matrix}\right.$

So for any two numbers $a$ and $b$,

$\left\mid a - b \right\mid$ is either equal to $a - b$ if that difference is positive or it is equal to $- \left(a - b\right)$ if the difference $a - b$ is negative.

$\pi$ is less than $11$, so $11 - \pi$ is already positive and

$\left\mid 11 - \pi \right\mid = 11 - \pi$

Bonus Example

$\left\mid 2 - \pi \right\mid$

$\pi$ is greater than $2$, so $2 - \pi$ is a negative number and the absolute value of a negative number is the opposite of that number:

$\left\mid 2 - \pi \right\mid = - \left(2 - \pi\right)$

Now we can rewrites $- \left(2 - \pi\right) = - 2 + \pi = \pi - 2$

So
$\left\mid 2 - \pi \right\mid = \pi - 2$

(It is worth trying to remember that $- \left(a - b\right)$ is always equal to $b - a$. That means: if we reverse the order of subtraction, we change the sign of the answer.)