Scanned handwriting in Tiff - DPI/pixel dimensions requirements for Printing

Namaste'
I am preparing to have a book printed of my Teacher's sayings in His own handwriting from His diaries.
The sayings were in ballpoint pen and some 20 years old.
We scanned them by a Greyscale hand scanner in 300dpi.
I have since cleaned and cropped them, so the 300 dpi standard is no longer there.
Since they are old, done with ball pen and not very thick, it is not realistic to take them "out" of their context, so they are on white background.
When I look at the scans info, it says 400dpi (the handwriting and the white background) but when I look at what the pixel dimensions say, they are all under 1 mb, mostly in the 300's to 700's k.
I do not understand this.
I was told 240dpi smallest.
What is the relation of pixel dimension to dpi? And how do I know this is enough?
Can anyone help clear this up for me?
When I take them down to the local printer and run them on their machine,for testing,  the images look fine.
I am using PSCS3.
Thank you.
A-Girl

When I scan linework art like signatures, handwriting, pen-and-ink drawings, etc., I set the scanner for 2400 PPI at print size, 1-bit/lineart/monochromatic/bw mode (your scanner software should call it one of these, the important bit is that it is NOT greyscale mode).
The reason for this is most imagesetters and platesetters output at either 2400 or 2540 DPI, so scanning at or close to the output resolution provides the crispest appearance. If you are outputting to a laser printer or other desktop device you could scan at its output resolution, 600 for example, but a 2400 PPi 1-bit file is not large at all so why not "future proof" your scans so if you get them professionally output later they are at maximum quality.
Using a 1-bit file eliminates any soft edges as you would have with a greyscale image, and 1-bits can easily be made to have a transparent background so placing them into a layout is a piece of cake.
My best advice to you is to detemine your output size, then re-scan at 2400 PPI at the correct size.
To your other question, pixel dimensions refers to the actual number of pixels in the image,  and is the only true measurement of resolution for a digital image.  Until you determine the print size PPI (pixels per inch) is irrelevant, and the PPI will change based on the output size: if you have an image that is 2000 pixels wide and you  print it at 10 inches then your PPI is 200 (2000 / 10). If you output at  5 inches then the PPI is 400 (2000 / 5).
DPI (dots per inch) refers to the resolution of an output device. The two are commonly used to mean the same thing, but they are not synonyms -- digital images contain only pixels, never dots, and printers output with dots, never pixels.

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