diff --git a/crates/print/src/sheets.rs b/crates/print/src/sheets.rs
--- a/crates/print/src/sheets.rs
+++ b/crates/print/src/sheets.rs
@@ -1038,6 +1038,21 @@ pub(crate) fn plan(sheets: &[Sheet], paper: (f64, f64), fit: Fit) -> Result<Vec<
                 if scale >= 1.0 && close((w, h), paper) {
                     None
                 } else {
+                    // The matrix is written with at most four decimals and a PDF real has no
+                    // exponent, so a scale that rounds away prints nothing at all and one that
+                    // rounds up prints the wrong size. Refuse both, the way a nondefault
+                    // UserUnit is refused: an error, never a job that spools a blank page.
+                    let written = number(scale).parse::<f64>().unwrap_or(0.0);
+                    if written <= 0.0 || (written - scale).abs() > scale * 0.01 {
+                        return Err(Error::Spool(format!(
+                            "shrink to fit cannot place sheet {} ({:.2} x {:.2} in) on the {:.2} x {:.2} in paper; nothing was sent",
+                            i + 1,
+                            w / 72.0,
+                            h / 72.0,
+                            pw / 72.0,
+                            ph / 72.0
+                        )));
+                    }
                     let [x0, y0, x1, y1] = sheet.bounds;
                     let (cw, ch) = (x1 - x0, y1 - y0);
                     // The paper in the page's unrotated space.
diff --git a/crates/print/src/tests/windows_native.rs b/crates/print/src/tests/windows_native.rs
--- a/crates/print/src/tests/windows_native.rs
+++ b/crates/print/src/tests/windows_native.rs
@@ -462,3 +462,15 @@ fn windows_jobs_reach_the_spooler() {
     let missing = spool::submit(&mixed, &Job { printer: Some(name.into()), ..Job::default() });
     assert!(matches!(missing, Err(Error::Spool(ref m)) if m.contains(name)), "{missing:?}");
 }
+
+#[test]
+fn shrink_to_fit_refuses_a_sheet_the_output_cannot_represent() {
+    use crate::sheets::{Fit, plan, read};
+    // A runaway-zoom export: 16 000 000 pt wide. Written with four decimals the scale would be
+    // "0" -- a singular matrix, a blank page, reported back as a spooled job.
+    let huge = TestPage { media: Some([0.0, 0.0, 16_000_000.0, 792.0]), ..LETTER };
+    let pdf = test_pdf(&[huge], false);
+    let sheets = read(&pdf).unwrap();
+    let refused = plan(&sheets.sheets, (612.0, 792.0), Fit::Shrink { margin: 18.0 });
+    assert!(matches!(refused, Err(Error::Spool(ref m)) if m.contains("shrink")), "{refused:?}");
+}