diff --git a/src/tag/scalar/float_core.ts b/src/tag/scalar/float_core.ts
index 9293717b..b7a18312 100644
--- a/src/tag/scalar/float_core.ts
+++ b/src/tag/scalar/float_core.ts
@@ -50,8 +50,20 @@ const floatCoreTag = defineScalarTag('tag:yaml.org,2002:float', {
   // ('.inf'/'.nan' start with '.').
   implicitFirstChars: ['-', '+', '.', ...'0123456789'],
   resolve: resolveYamlFloat,
-  identify: (object) => Object.prototype.toString.call(object) === '[object Number]' &&
-    (object % 1 !== 0 || Object.is(object, -0)),
+  identify: (object) =>
+    // No ancient boxed numbers support
+    typeof object === 'number' &&
+    (
+      // We land here all numbers, not handled (declined) by !!int `.identify`
+      // The same condition as for !!int, but reversed.
+
+      // Filter out integers...
+      !Number.isInteger(object) ||
+      // but allow negative zero
+      Object.is(object, -0) ||
+      // and integers with exponential form
+      object.toString(10).indexOf('e') >= 0
+    ),
   represent: representYamlFloat
 })
 
diff --git a/src/tag/scalar/float_json.ts b/src/tag/scalar/float_json.ts
index 8c28e557..ad222630 100644
--- a/src/tag/scalar/float_json.ts
+++ b/src/tag/scalar/float_json.ts
@@ -56,8 +56,20 @@ const floatJsonTag = defineScalarTag('tag:yaml.org,2002:float', {
   // Superset of source.charAt(0) over all matched inputs: optional '-' or digit.
   implicitFirstChars: ['-', ...'0123456789'],
   resolve: resolveYamlFloat,
-  identify: (object) => Object.prototype.toString.call(object) === '[object Number]' &&
-    (object % 1 !== 0 || Object.is(object, -0)),
+  identify: (object) =>
+    // No ancient boxed numbers support
+    typeof object === 'number' &&
+    (
+      // We land here all numbers, not handled (declined) by !!int `.identify`
+      // The same condition as for !!int, but reversed.
+
+      // Filter out integers...
+      !Number.isInteger(object) ||
+      // but allow negative zero
+      Object.is(object, -0) ||
+      // and integers with exponential form
+      object.toString(10).indexOf('e') >= 0
+    ),
   represent: representYamlFloat
 })
 
diff --git a/src/tag/scalar/float_yaml11.ts b/src/tag/scalar/float_yaml11.ts
index ec4b616b..6fd27e64 100644
--- a/src/tag/scalar/float_yaml11.ts
+++ b/src/tag/scalar/float_yaml11.ts
@@ -57,8 +57,20 @@ const floatYaml11Tag = defineScalarTag('tag:yaml.org,2002:float', {
   // ('.inf'/'.nan' start with '.').
   implicitFirstChars: ['-', '+', '.', ...'0123456789'],
   resolve: resolveYamlFloat,
-  identify: (object) => Object.prototype.toString.call(object) === '[object Number]' &&
-    (object % 1 !== 0 || Object.is(object, -0)),
+  identify: (object) =>
+    // No ancient boxed numbers support
+    typeof object === 'number' &&
+    (
+      // We land here all numbers, not handled (declined) by !!int `.identify`
+      // The same condition as for !!int, but reversed.
+
+      // Filter out integers...
+      !Number.isInteger(object) ||
+      // but allow negative zero
+      Object.is(object, -0) ||
+      // and integers with exponential form
+      object.toString(10).indexOf('e') >= 0
+    ),
   represent: representYamlFloat
 })
 
diff --git a/src/tag/scalar/int_core.ts b/src/tag/scalar/int_core.ts
index 573091c9..e097e8bf 100644
--- a/src/tag/scalar/int_core.ts
+++ b/src/tag/scalar/int_core.ts
@@ -53,8 +53,13 @@ const intCoreTag = defineScalarTag('tag:yaml.org,2002:int', {
   // Superset of source.charAt(0) over all matched inputs: optional sign + decimal digit.
   implicitFirstChars: ['-', '+', ...'0123456789'],
   resolve: resolveYamlInteger,
-  identify: (object) => Object.prototype.toString.call(object) === '[object Number]' &&
-    (object % 1 === 0 && !Object.is(object, -0)),
+  identify: (object) =>
+    // No ancient boxed numbers support
+    Number.isInteger(object) &&
+    // Negative zero => !!float
+    !Object.is(object, -0) &&
+    // Exponential form => !!float, round-trip for !!int 1e21 will be broken
+    object.toString(10).indexOf('e') < 0,
   represent: (object: number) => object.toString(10)
 })
 
diff --git a/src/tag/scalar/int_json.ts b/src/tag/scalar/int_json.ts
index c4d9eddf..393292c9 100644
--- a/src/tag/scalar/int_json.ts
+++ b/src/tag/scalar/int_json.ts
@@ -48,8 +48,13 @@ const intJsonTag = defineScalarTag('tag:yaml.org,2002:int', {
   // Superset of source.charAt(0) over all matched inputs: optional '-' or digit.
   implicitFirstChars: ['-', ...'0123456789'],
   resolve: resolveYamlInteger,
-  identify: (object) => Object.prototype.toString.call(object) === '[object Number]' &&
-    (object % 1 === 0 && !Object.is(object, -0)),
+  identify: (object) =>
+    // No ancient boxed numbers support
+    Number.isInteger(object) &&
+    // Negative zero => !!float
+    !Object.is(object, -0) &&
+    // Exponential form => !!float, round-trip for !!int 1e21 will be broken
+    object.toString(10).indexOf('e') < 0,
   represent: (object: number) => object.toString(10)
 })
 
diff --git a/src/tag/scalar/int_yaml11.ts b/src/tag/scalar/int_yaml11.ts
index 84263338..a4c30326 100644
--- a/src/tag/scalar/int_yaml11.ts
+++ b/src/tag/scalar/int_yaml11.ts
@@ -47,8 +47,13 @@ const intYaml11Tag = defineScalarTag('tag:yaml.org,2002:int', {
   // Superset of source.charAt(0) over all matched inputs: optional sign + decimal digit.
   implicitFirstChars: ['-', '+', ...'0123456789'],
   resolve: resolveYamlInteger,
-  identify: (object) => Object.prototype.toString.call(object) === '[object Number]' &&
-    (object % 1 === 0 && !Object.is(object, -0)),
+  identify: (object) =>
+    // No ancient boxed numbers support
+    Number.isInteger(object) &&
+    // Negative zero => !!float
+    !Object.is(object, -0) &&
+    // Exponential form => !!float, round-trip for !!int 1e21 will be broken
+    object.toString(10).indexOf('e') < 0,
   represent: (object: number) => object.toString(10)
 })
 
diff --git a/test/core/tags/int.test.mjs b/test/core/tags/int.test.mjs
index 5a4247fe..68c26487 100644
--- a/test/core/tags/int.test.mjs
+++ b/test/core/tags/int.test.mjs
@@ -39,6 +39,27 @@ describe('tags/int', () => {
         assert.deepStrictEqual(load(dump(expected, { schema }), { schema }), expected)
       })
 
+      it(`${name} round-trip of large integers`, () => {
+        // Integers at or above 1e21 stringify in exponential notation
+        // ('1e+21'), which is not valid `!!int` text. They must round-trip
+        // through the float tag rather than being dumped as `!!int '1e+21'`.
+
+        // Should round-trip as !!int
+        assert.strictEqual(dump(1e20, { schema }), '100000000000000000000\n')
+        assert.strictEqual(load(dump(1e20, { schema }), { schema }), 1e20)
+        assert.strictEqual(dump(-1e20, { schema }), '-100000000000000000000\n')
+        assert.strictEqual(load(dump(-1e20, { schema }), { schema }), -1e20)
+
+        // Should round-trip as !!float
+        assert.strictEqual(dump(1e21, { schema }), '1.e+21\n')
+        assert.strictEqual(load(dump(1e21, { schema }), { schema }), 1e21)
+        assert.strictEqual(dump(-1e21, { schema }), '-1.e+21\n')
+        assert.strictEqual(load(dump(-1e21, { schema }), { schema }), -1e21)
+
+        assert.strictEqual(load(dump(Number.MAX_VALUE, { schema }), { schema }), Number.MAX_VALUE)
+        assert.strictEqual(load(dump(-Number.MAX_VALUE, { schema }), { schema }), -Number.MAX_VALUE)
+      })
+
       it(`${name} fail explicit tag`, () => {
         assert.throws(() => load('!!int 1.5', { schema }), /cannot resolve/)
       })