Question

Express the quantity without using absolute value

$\left|\pi -3\right|$

Short answer

The quantity of$\left|\pi -3\right|\mathrm{is}\pi -3$.

Step-by-step solution

Step 1. Apply the concept of absolute value.

If a is a real number, then the absolute value of a is given by:

$\left|a\right|=\left\{\begin{array}{l}a\text{;if}a\ge 0\\ -a\text{;if}a<0\end{array}\right.$

Step 2. Analyze the given value.

Given$\left|\pi -3\right|$

Here the value inside modulus is $\left|\pi -3\right|$.

$\begin{array}{l}\pi \approx 3.14>3\\ \Rightarrow \pi -3>0\end{array}$

Step 3. Write without using absolute value.

$\left|\pi -3\right|=\pi -\mathrm{3.................}[\pi -3>0]$