diff --git a/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
index dca1cad29f..4471f21c63 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
@@ -1784,7 +1784,10 @@ protected JsonToken _handleInvalidNumberStart(int ch, final boolean negative, fi
         if (!isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature()) && hasSign && !negative) {
             reportUnexpectedNumberChar('+', "JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
         }
-        reportUnexpectedNumberChar(ch, "expected digit (0-9) to follow minus sign, for valid numeric value");
+        final String message = negative ?
+                "expected digit (0-9) to follow minus sign, for valid numeric value" :
+                "expected digit (0-9) for valid numeric value";
+        reportUnexpectedNumberChar(ch, message);
         return null;
     }
 
diff --git a/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
index 1fdc3b363c..7d5f255c85 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
@@ -2273,7 +2273,10 @@ protected JsonToken _handleInvalidNumberStart(int ch, final boolean neg, final b
         if (!isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature()) && hasSign && !neg) {
             reportUnexpectedNumberChar('+', "JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
         }
-        reportUnexpectedNumberChar(ch, "expected digit (0-9) to follow minus sign, for valid numeric value");
+        final String message = neg ?
+                "expected digit (0-9) to follow minus sign, for valid numeric value" :
+                "expected digit (0-9) for valid numeric value";
+        reportUnexpectedNumberChar(ch, message);
         return null;
     }
 
diff --git a/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
index 8a4dafc930..ee7e8a595e 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
@@ -2912,7 +2912,10 @@ protected JsonToken _handleInvalidNumberStart(int ch, final boolean neg, final b
         if (!isEnabled(JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS.mappedFeature()) && hasSign && !neg) {
             reportUnexpectedNumberChar('+', "JSON spec does not allow numbers to have plus signs: enable `JsonReadFeature.ALLOW_LEADING_PLUS_SIGN_FOR_NUMBERS` to allow");
         }
-        reportUnexpectedNumberChar(ch, "expected digit (0-9) to follow minus sign, for valid numeric value");
+        final String message = neg ?
+                "expected digit (0-9) to follow minus sign, for valid numeric value" :
+                "expected digit (0-9) for valid numeric value";
+        reportUnexpectedNumberChar(ch, message);
         return null;
     }
 
diff --git a/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java
index 2e7bfc278c..ac4c904cd8 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/async/NonBlockingJsonParser.java
@@ -1730,17 +1730,27 @@ protected JsonToken _finishFloatFraction() throws IOException
         int outPtr = _textBuffer.getCurrentSegmentSize();
 
         // caller guarantees at least one char; also, sign-extension not needed here
-        int ch;
-        while (((ch = _inputBuffer[_inputPtr++]) >= INT_0) && (ch <= INT_9)) {
-            ++fractLen;
-            if (outPtr >= outBuf.length) {
-                outBuf = _textBuffer.expandCurrentSegment();
-            }
-            outBuf[outPtr++] = (char) ch;
-            if (_inputPtr >= _inputEnd) {
-                _textBuffer.setCurrentLength(outPtr);
-                _fractLength = fractLen;
-                return JsonToken.NOT_AVAILABLE;
+        int ch = _inputBuffer[_inputPtr++];
+        boolean loop = true;
+        while (loop) {
+            if (ch >= INT_0 && ch <= INT_9) {
+                ++fractLen;
+                if (outPtr >= outBuf.length) {
+                    outBuf = _textBuffer.expandCurrentSegment();
+                }
+                outBuf[outPtr++] = (char) ch;
+                if (_inputPtr >= _inputEnd) {
+                    _textBuffer.setCurrentLength(outPtr);
+                    _fractLength = fractLen;
+                    return JsonToken.NOT_AVAILABLE;
+                }
+                ch = _inputBuffer[_inputPtr++];
+            } else if (ch == 'f' || ch == 'd' || ch == 'F' || ch == 'D') {
+                reportUnexpectedNumberChar(ch, "JSON does not support parsing numbers that have 'f' or 'd' suffixes");
+            } else if (ch == INT_PERIOD) {
+                reportUnexpectedNumberChar(ch, "Cannot parse number with more than one decimal point");
+            } else {
+                loop = false;
             }
         }
         
diff --git a/src/test/java/com/fasterxml/jackson/core/json/async/AsyncNonStandardNumberParsingTest.java b/src/test/java/com/fasterxml/jackson/core/json/async/AsyncNonStandardNumberParsingTest.java
index 304ac16c0d..bfef6adc8f 100644
--- a/src/test/java/com/fasterxml/jackson/core/json/async/AsyncNonStandardNumberParsingTest.java
+++ b/src/test/java/com/fasterxml/jackson/core/json/async/AsyncNonStandardNumberParsingTest.java
@@ -62,8 +62,6 @@ public void testNegativeHexadecimal() throws Exception
         }
     }
 
-    //next 2 tests do not work as expected
-    /*
     public void testFloatMarker() throws Exception
     {
         final String JSON = "[ -0.123f ]";
@@ -97,7 +95,22 @@ public void testDoubleMarker() throws Exception
             p.close();
         }
     }
-    */
+
+    public void test2DecimalPoints() throws Exception {
+        final String JSON = "[ -0.123.456 ]";
+
+        // without enabling, should get an exception
+        AsyncReaderWrapper p = createParser(DEFAULT_F, JSON, 1);
+        assertToken(JsonToken.START_ARRAY, p.nextToken());
+        try {
+            p.nextToken();
+            fail("Expected exception");
+        } catch (Exception e) {
+            verifyException(e, "Unexpected character ('.'");
+        } finally {
+            p.close();
+        }
+    }
 
     /**
      * The format ".NNN" (as opposed to "0.NNN") is not valid JSON, so this should fail
diff --git a/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java b/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java
index d2983fed0c..585f83995a 100644
--- a/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java
+++ b/src/test/java/com/fasterxml/jackson/core/read/NonStandardNumberParsingTest.java
@@ -80,6 +80,17 @@ public void testDoubleMarker() throws Exception {
         }
     }
 
+    public void test2DecimalPoints() throws Exception {
+        for (int mode : ALL_MODES) {
+            try (JsonParser p = createParser(mode, " -0.123.456 ")) {
+                p.nextToken();
+                fail("Should not pass");
+            } catch (JsonParseException e) {
+                verifyException(e, "Unexpected character ('.'");
+            }
+        }
+    }
+
     /**
      * The format ".NNN" (as opposed to "0.NNN") is not valid JSON, so this should fail
      */