Evaluate (8.25 + 0.544) / (1 - 0.544).

Step-by-step solution

1. 1

   Work the numerator and denominator separately first. Order of operations puts the grouped sums ahead of the division, so neither can be split up:

   $8.25+0.544=8.794,\qquad 1-0.544=0.456$

2. 2

   Set up the division.

   $\frac{8.794}{0.456}$

   The denominator is less than $1$, so the quotient must be larger than $8.794$ — a useful expectation before touching a calculator.

3. 3

   Clear the decimals to make the division exact. Multiply numerator and denominator by $1000$:

   $\frac{8.794}{0.456}=\frac{8794}{456}=\frac{4397}{228}$

   This exact fraction is the honest form of the answer; the decimal below is a rounding of it.

4. 4

   Divide and round. Long division gives

   $\frac{4397}{228}=19.285087719\ldots$

   so to four decimal places the value is $19.2851$ (the fifth digit is an $8$, which rounds the fourth digit $0$ up to $1$).

5. 5

   Check the magnitude. Estimating, $0.456$ is close to $0.45$, and $8.794/0.45\approx19.5$. The computed $19.2851$ is right beside that estimate, so no decimal point has slipped.