diff --git a/datafusion/sql/src/expr/value.rs b/datafusion/sql/src/expr/value.rs
index e1a6965fca590..25c912eddd4fc 100644
--- a/datafusion/sql/src/expr/value.rs
+++ b/datafusion/sql/src/expr/value.rs
@@ -108,17 +108,21 @@ impl<S: ContextProvider> SqlToRel<'_, S> {
         }
 
         if self.options.parse_float_as_decimal {
-            parse_decimal(
+            let decimal = parse_decimal(
                 unsigned_number,
                 negative,
                 self.options.trim_decimal_literal_trailing_zeros,
-            )
+            );
+            match decimal {
+                Err(DataFusionError::NotImplemented(_))
+                    if unsigned_number.contains(['.', 'e', 'E']) =>
+                {
+                    parse_float(&signed_number)
+                }
+                result => result,
+            }
         } else {
-            signed_number.parse::<f64>().map(lit).map_err(|_| {
-                DataFusionError::from(ParserError(format!(
-                    "Cannot parse {signed_number} as f64"
-                )))
-            })
+            parse_float(&signed_number)
         }
     }
 
@@ -379,6 +383,12 @@ fn bigint_to_i256(v: &BigInt) -> Option<i256> {
     }
 }
 
+fn parse_float(signed_number: &str) -> Result<Expr> {
+    signed_number.parse::<f64>().map(lit).map_err(|_| {
+        DataFusionError::from(ParserError(format!("Cannot parse {signed_number} as f64")))
+    })
+}
+
 fn parse_decimal(
     unsigned_number: &str,
     negative: bool,
diff --git a/datafusion/sql/tests/sql_integration.rs b/datafusion/sql/tests/sql_integration.rs
index 390e8cc017921..a83d070355e0b 100644
--- a/datafusion/sql/tests/sql_integration.rs
+++ b/datafusion/sql/tests/sql_integration.rs
@@ -26,7 +26,9 @@ use std::vec;
 
 use arrow::datatypes::{TimeUnit::Nanosecond, *};
 use common::MockContextProvider;
-use datafusion_common::{DFSchema, DataFusionError, Result, assert_contains};
+use datafusion_common::{
+    DFSchema, DataFusionError, Result, ScalarValue, assert_contains,
+};
 use datafusion_expr::{
     ColumnarValue, CreateIndex, DdlStatement, Expr, HigherOrderFunctionArgs,
     HigherOrderReturnFieldArgs, HigherOrderSignature, HigherOrderUDF, HigherOrderUDFImpl,
@@ -194,6 +196,36 @@ fn parse_decimals_9() {
     );
 }
 
+#[test]
+fn parse_decimal_out_of_range_float_falls_back_to_float64() {
+    let sql = "SELECT 1.7976931348623157e+308, 2.2250738585072014e-308";
+    let options = parse_decimals_parser_options();
+    let plan = logical_plan_with_options(sql, options).unwrap();
+    let LogicalPlan::Projection(projection) = plan else {
+        panic!("expected a projection")
+    };
+    let values = projection
+        .expr
+        .iter()
+        .map(|expr| match expr {
+            Expr::Literal(ScalarValue::Float64(Some(value)), _) => value.to_bits(),
+            _ => panic!("expected Float64 literals, got {expr}"),
+        })
+        .collect::<Vec<_>>();
+    assert_eq!(values, [f64::MAX.to_bits(), f64::MIN_POSITIVE.to_bits()]);
+}
+
+#[test]
+fn parse_decimal_out_of_range_integer_remains_an_error() {
+    let sql = format!("SELECT {}", "1".repeat(77));
+    let options = parse_decimals_parser_options();
+    let error = logical_plan_with_options(&sql, options).unwrap_err();
+    assert_contains!(
+        error.to_string(),
+        "Decimal precision 77 exceeds the maximum supported precision: 76"
+    );
+}
+
 #[test]
 fn parse_decimals_trim_insignificant_trailing_zeros() {
     let sql = "SELECT 10.00, 10.10, 0.00100, 100.0001, 1.2300e2";