41.- Think you want to print out a photograph with a size of DIN A4: 210 × 297 mm

maintaining a printing quality of 200 dpi. Which resolution would the image need?

Required Resolution for Printing DIN A4 at 200 dpi

To print a photograph at DIN A4 size ($210 \text{ mm} \times 297 \text{ mm}$) while maintaining a printing quality of 200 dpi (dots per inch), the digital image must have a resolution of approximately $1654 \times 2339$ pixels.

This calculation is carried out in two main steps:

Step 1: Convert Dimensions from Millimeters to Inches

Since the printing quality is measured in dpi (dots per inch), we must first convert the paper dimensions from the metric system (millimeters) to the imperial system (inches). We use the equivalence: $1 \text{ inch} = 25.4 \text{ mm}$.

• Width in Inches: $\frac{210 \text{ mm}}{25.4 \text{ mm/in}} \approx 8.2677 \text{ in}$

• Height in Inches: $\frac{297 \text{ mm}}{25.4 \text{ mm/in}} \approx 11.6929 \text{ in}$

Step 2: Calculate Pixels by Multiplying by the DPI

Once the dimensions are in inches, each dimension is multiplied by the quality requirement (200 dpi) to obtain the total number of pixels needed for that dimension.

• Width Pixels: $8.2677 \text{ in} \times 200 \text{ dpi} \approx 1653.54 \rightarrow \mathbf{1654 \text{ pixels}}$

• Height Pixels: $11.6929 \text{ in} \times 200 \text{ dpi} \approx 2338.58 \rightarrow \mathbf{2339 \text{ pixels}}$

Therefore, the necessary resolution is $1654 \times 2339$ pixels.