diff --git a/src/main/java/com/fasterxml/jackson/core/StreamReadCapability.java b/src/main/java/com/fasterxml/jackson/core/StreamReadCapability.java
index 63d8b50282..5519e2be37 100644
--- a/src/main/java/com/fasterxml/jackson/core/StreamReadCapability.java
+++ b/src/main/java/com/fasterxml/jackson/core/StreamReadCapability.java
@@ -48,6 +48,23 @@ public enum StreamReadCapability
      * This capability is true for many textual formats like CSV, Properties and XML.
      */
     UNTYPED_SCALARS(false),
+
+    /**
+     * Capability that indicates that data format may report floats
+     * as a non-exact {@link com.fasterxml.jackson.core.JsonParser.NumberType},
+     * due to prohibitively expensive parsing costs of determing the precision
+     * upfront. For example, JSON numbers may be reported as
+     * {@link com.fasterxml.jackson.core.JsonParser.NumberType#DOUBLE}
+     * even if they would not fit into a 64-bit double without precision
+     * loss. Methods like {@link JsonParser#getNumberValueExact()} or
+     * {@link JsonParser#getValueAsString()} still report values without
+     * precision loss.
+     *
+     * Capability is false for text formats JSON, but true for binary formats
+     * like Smile, MessagePack, etc., where type is precisely and inexpensively
+     * signaled by a tag.
+     */
+    EXACT_FLOATS(false)
     ;
 
     /**
diff --git a/src/test/java/com/fasterxml/jackson/failing/ParserPrecisionLoss733Test.java b/src/test/java/com/fasterxml/jackson/failing/ParserPrecisionLoss733Test.java
new file mode 100644
index 0000000000..fd39060fc8
--- /dev/null
+++ b/src/test/java/com/fasterxml/jackson/failing/ParserPrecisionLoss733Test.java
@@ -0,0 +1,47 @@
+package com.fasterxml.jackson.failing;
+
+import com.fasterxml.jackson.core.BaseTest;
+import com.fasterxml.jackson.core.JsonFactory;
+import com.fasterxml.jackson.core.JsonGenerator;
+import com.fasterxml.jackson.core.JsonParser;
+
+import java.io.ByteArrayOutputStream;
+import java.io.StringWriter;
+
+public class ParserPrecisionLoss733Test extends BaseTest {
+    final JsonFactory JSON_F = newStreamFactory();
+
+    /**
+     * Attempt to pass a BigDecimal value through without losing precision,
+     * e.g. for pretty printing a file.
+     */
+    public void testCopyCurrentEventBigDecimal() throws Exception {
+        String input = "1e999";
+        JsonParser parser = JSON_F.createParser(input);
+        parser.nextToken();
+        StringWriter stringWriter = new StringWriter();
+        JsonGenerator generator = JSON_F.createGenerator(stringWriter);
+        generator.copyCurrentEvent(parser);
+        parser.close();
+        generator.close();
+        String actual = stringWriter.toString();
+        assertEquals(input, actual);
+    }
+
+    /**
+     * Same as {@link #testCopyCurrentEventBigDecimal()} using copyCurrentStructure instead.
+     */
+    public void testCopyCurrentStructureBigDecimal() throws Exception {
+        String input = "[1e999]";
+        JsonParser parser = JSON_F.createParser(input);
+        parser.nextToken();
+        StringWriter stringWriter = new StringWriter();
+        JsonGenerator generator = JSON_F.createGenerator(stringWriter);
+        generator.copyCurrentStructure(parser);
+        parser.close();
+        generator.close();
+        String actual = stringWriter.toString();
+        assertEquals(input, actual);
+    }
+
+}