42.- Which resolution would the same picture need to have a 300 dpi picture?

 

The same picture, with a size of DIN A4 ($210 \text{ mm} \times 297 \text{ mm}$), would need a resolution of approximately $2480 \times 3508$ pixels to maintain a printing quality of 300 dpi (dots per inch).

---

 Calculation Steps

The calculation follows the principle of converting the physical dimensions (mm) into inches and then multiplying by the desired printing resolution (dpi).

Step 1: Convert DIN A4 Dimensions to Inches

The conversion factor used is $1 \text{ inch} = 25.4 \text{ mm}$.

Dimension	Calculation	Result
Width (210 mm)	$\frac{210 \text{ mm}}{25.4 \text{ mm/in}} \approx 8.2677 \text{ in}$	$8.2677 \text{ inches}$
Height (297 mm)	$\frac{297 \text{ mm}}{25.4 \text{ mm/in}} \approx 11.6929 \text{ in}$	$11.6929 \text{ inches}$

Step 2: Calculate Required Resolution (Pixels)

The required number of pixels is found by multiplying the size in inches by the quality requirement of 300 dpi.

$$\text{Resolution (pixels)} = \text{Size (in)} \times 300 \text{ dpi}$$

Dimension	Calculation	Result (Rounded)
Width Pixels	$8.2677 \text{ in} \times 300 \text{ dpi} \approx 2480.31$	$2480 \text{ pixels}$
Height Pixels	$11.6929 \text{ in} \times 300 \text{ dpi} \approx 3507.87$	$3508 \text{ pixels}$