diff --git a/decode.go b/decode.go
index d366f1d..cd21bee 100644
--- a/decode.go
+++ b/decode.go
@@ -306,12 +306,26 @@ func parseIntBin(b []byte) (int64, error) {
 	return i, nil
 }
 
+func isSign(b byte) bool {
+	return b == '+' || b == '-'
+}
+
 func parseIntDec(b []byte) (int64, error) {
 	cleaned, err := checkAndRemoveUnderscoresIntegers(b)
 	if err != nil {
 		return 0, err
 	}
 
+	startIdx := 0
+
+	if isSign(cleaned[0]) {
+		startIdx++
+	}
+
+	if len(cleaned) > startIdx+1 && cleaned[startIdx] == '0' {
+		return 0, newDecodeError(b, "leading zero not allowed on decimal number")
+	}
+
 	i, err := strconv.ParseInt(string(cleaned), 10, 64)
 	if err != nil {
 		return 0, newDecodeError(b, "couldn't parse decimal number: %w", err)
diff --git a/parser.go b/parser.go
index 0d2beb9..67353c8 100644
--- a/parser.go
+++ b/parser.go
@@ -958,7 +958,7 @@ byteLoop:
 func (p *parser) scanIntOrFloat(b []byte) (ast.Reference, []byte, error) {
 	i := 0
 
-	if len(b) > 2 && b[0] == '0' && b[1] != '.' {
+	if len(b) > 2 && b[0] == '0' && b[1] != '.' && b[1] != 'e' {
 		var isValidRune validRuneFn
 
 		switch b[1] {
diff --git a/toml_testgen_test.go b/toml_testgen_test.go
index 39fddb6..3f3bcf5 100644
--- a/toml_testgen_test.go
+++ b/toml_testgen_test.go
@@ -506,13 +506,11 @@ func TestTOMLTest_Invalid_Integer_LeadingZero2(t *testing.T) {
 }
 
 func TestTOMLTest_Invalid_Integer_LeadingZeroSign1(t *testing.T) {
-	t.Skip("FIXME")
 	input := "leading-zero-sign-1 = -01\n"
 	testgenInvalid(t, input)
 }
 
 func TestTOMLTest_Invalid_Integer_LeadingZeroSign2(t *testing.T) {
-	t.Skip("FIXME")
 	input := "leading-zero-sign-2 = +01\n"
 	testgenInvalid(t, input)
 }
@@ -1155,7 +1153,6 @@ func TestTOMLTest_Valid_Float_Underscore(t *testing.T) {
 }
 
 func TestTOMLTest_Valid_Float_Zero(t *testing.T) {
-	t.Skip("FIXME")
 	input := "zero = 0.0\nsigned-pos = +0.0\nsigned-neg = -0.0\nexponent = 0e0\nexponent-two-0 = 0e00\nexponent-signed-pos = +0e0\nexponent-signed-neg = -0e0\n"
 	jsonRef := "{\n  \"zero\": {\n    \"type\": \"float\",\n    \"value\": \"0\"\n  },\n  \"signed-pos\": {\n    \"type\": \"float\",\n    \"value\": \"0\"\n  },\n  \"signed-neg\": {\n    \"type\": \"float\",\n    \"value\": \"0\"\n  },\n  \"exponent\": {\n    \"type\": \"float\",\n    \"value\": \"0\"\n  },\n  \"exponent-two-0\": {\n    \"type\": \"float\",\n    \"value\": \"0\"\n  },\n  \"exponent-signed-pos\": {\n    \"type\": \"float\",\n    \"value\": \"0\"\n  },\n  \"exponent-signed-neg\": {\n    \"type\": \"float\",\n    \"value\": \"0\"\n  }\n}\n"
 	testgenValid(t, input, jsonRef)
diff --git a/unmarshaler_test.go b/unmarshaler_test.go
index 2f59d55..4374d87 100644
--- a/unmarshaler_test.go
+++ b/unmarshaler_test.go
@@ -149,6 +149,11 @@ func TestUnmarshal_Floats(t *testing.T) {
 			input:    `-2E-2`,
 			expected: -2e-2,
 		},
+		{
+			desc:     "float exponent zero",
+			input:    `0e0`,
+			expected: 0.0,
+		},
 		{
 			desc:     "float fractional with exponent",
 			input:    `6.626e-34`,