diff --git a/src/items/mod.rs b/src/items/mod.rs
index 9a9794a..f43f661 100644
--- a/src/items/mod.rs
+++ b/src/items/mod.rs
@@ -145,9 +145,9 @@ where
 /// following two forms:
 ///
 /// - 0
-/// - [+-][1-9][0-9]*
+/// - [+-]?[1-9][0-9]*
 ///
-/// Inputs like [+-]0[0-9]* (e.g., `+012`) are therefore rejected. We provide a
+/// Inputs like [+-]?0[0-9]* (e.g., `+012`) are therefore rejected. We provide a
 /// custom implementation to support such zero-prefixed integers.
 fn dec_int<'a, E>(input: &mut &'a str) -> winnow::Result<i32, E>
 where
@@ -175,6 +175,23 @@ where
         .parse_next(input)
 }
 
+/// Parse a float number.
+///
+/// Rationale for not using `winnow::ascii::float`: the `float` parser provided
+/// by winnow accepts E-notation numbers (e.g., `1.23e4`), whereas GNU date
+/// rejects such numbers. To remain compatible with GNU date, we provide a
+/// custom implementation that only accepts inputs like [+-]?[0-9]+(\.[0-9]+)?.
+fn float<'a, E>(input: &mut &'a str) -> winnow::Result<f64, E>
+where
+    E: ParserError<&'a str>,
+{
+    (opt(one_of(['+', '-'])), digit1, opt(preceded('.', digit1)))
+        .void()
+        .take()
+        .verify_map(|s: &str| s.parse().ok())
+        .parse_next(input)
+}
+
 // Parse an item
 pub fn parse_one(input: &mut &str) -> ModalResult<Item> {
     trace(
diff --git a/src/items/relative.rs b/src/items/relative.rs
index 3a605a7..701a197 100644
--- a/src/items/relative.rs
+++ b/src/items/relative.rs
@@ -32,12 +32,12 @@
 //! > ‘this thursday’.
 
 use winnow::{
-    ascii::{alpha1, float},
+    ascii::alpha1,
     combinator::{alt, opt},
     ModalResult, Parser,
 };
 
-use super::{ordinal::ordinal, s};
+use super::{float, ordinal::ordinal, s};
 
 #[derive(Clone, Copy, Debug, PartialEq)]
 pub enum Relative {
diff --git a/src/lib.rs b/src/lib.rs
index 9d25616..3dc5a1a 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -165,7 +165,13 @@ mod tests {
 
         #[test]
         fn invalid_formats() {
-            let invalid_dts = vec!["NotADate", "202104", "202104-12T22:37:47"];
+            let invalid_dts = vec![
+                "NotADate",
+                "202104",
+                "202104-12T22:37:47",
+                "a774e26sec", // 774e26 is not a valid seconds value (we don't accept E-notation)
+                "12.",        // Invalid floating point number
+            ];
             for dt in invalid_dts {
                 assert_eq!(parse_datetime(dt), Err(ParseDateTimeError::InvalidInput));
             }