Question

Find the absolute change and the relative change in the following case. The number of daily newspapers in a country decreased from $2025$ in $1900$ to $1251$ in $2010$.

The absolute change is ___. (Simplify your answer. Write an integer or a decimal.)

The relative change is ___$\%$. (Round to the nearest integer as needed.)

• A. $-774$
• B. $-38$

Answer 1

Step 1: Find the absolute change.

The absolute change in a quantity is defined as the result of subtracting its initial value from its final value. It is given that the number of daily newspapers has changed from $2025$ (initial value) to $1251$ (final value). Thus, the absolute change is $1251-2025=-774$.

Step 2: Find the relative change.

The relative change in a quantity is defined as the ratio of the absolute change in it to its initial value. In the present situation, the relative change is the ratio of the absolute change $-774$ to the initial value $2025$.

Thus, the relative change is $\begin{array}{rcl}& =& \frac{-774}{2025}\times 100\%\end{array}$

$\begin{array}{rcl}& =& \frac{-774}{81}\times 4\%\\ & =& \frac{-86}{9}\times 4\%\\ & =& -\frac{344}{9}\%\\ & =& -38.22\%\end{array}$

Thus, the relative change rounded to the nearest integer is $-38\%$.

Hence, the absolute change is $\mathbf{-}\mathbf{774}$ and the relative change is $\mathbf{-}\mathbf{38}\mathbf{\%}$.