Straight answers
Can I use scratch paper on the digital SAT?
Yes. Scratch paper is provided at the test center for the digital SAT, so you work problems out by hand even though the test itself is on a screen. You bring pencils; you do not bring your own paper. Check your test-day instructions for the exact rules at your location.
A screen-based test does not mean mental-only math. Writing out steps is one of the most reliable ways to avoid arithmetic slips and to keep a multi-step problem straight, and nothing about the digital format discourages it.
The paper is for your working, so use it as a system rather than a pile. Number your notes to match the question number on screen. That way, if you flag a question and come back, your earlier work is one glance away instead of a mystery scribble.
On Reading and Writing, scratch paper helps in a different way: jotting a one-line prediction before you look at the choices, or writing A-B-C-D and crossing off eliminated options. That small habit keeps you from being pulled toward a choice that merely sounds good.
The rules about what happens to your scratch paper and what else is allowed at your seat are set by the test center and by College Board's test-day policies, so treat those instructions as the source of truth. If anything on this page and your admission-ticket instructions ever differ, follow the ticket.
Practice the way you will test. When you work Brainrise drills, keep a pencil and paper beside the screen and write the steps out, so doing it on test day is already routine.