diff --git a/question/type/numerical/question.php b/question/type/numerical/question.php
index 93d276af9ce..110cfdc02a9 100644
--- a/question/type/numerical/question.php
+++ b/question/type/numerical/question.php
@@ -320,10 +320,13 @@ class qtype_numerical_answer extends question_answer {
             throw new coding_exception('Cannot work out tolerance interval for answer *.');
         }
 
+        // Smallest number that, when added to 1, is different from 1.
+        $epsilon = pow(10, -1 * ini_get('precision'));
+
         // We need to add a tiny fraction depending on the set precision to make
         // the comparison work correctly, otherwise seemingly equal values can
         // yield false. See MDL-3225.
-        $tolerance = (float) $this->tolerance + pow(10, -1 * ini_get('precision'));
+        $tolerance = abs($this->tolerance) + $epsilon;
 
         switch ($this->tolerancetype) {
             case 1: case 'relative':
@@ -331,8 +334,7 @@ class qtype_numerical_answer extends question_answer {
                 return array($this->answer - $range, $this->answer + $range);
 
             case 2: case 'nominal':
-                $tolerance = $this->tolerance + pow(10, -1 * ini_get('precision')) *
-                        max(1, abs($this->answer));
+                $tolerance = $this->tolerance + $epsilon * max(abs($this->tolerance), abs($this->answer), $epsilon);
                 return array($this->answer - $tolerance, $this->answer + $tolerance);
 
             case 3: case 'geometric':
diff --git a/question/type/numerical/tests/answer_test.php b/question/type/numerical/tests/answer_test.php
index c3d276ae641..a74fed3c924 100644
--- a/question/type/numerical/tests/answer_test.php
+++ b/question/type/numerical/tests/answer_test.php
@@ -25,8 +25,10 @@
  */
 
 global $CFG;
+require_once($CFG->dirroot . '/question/engine/tests/helpers.php');
 require_once($CFG->dirroot . '/question/type/numerical/question.php');
 
+
 class qtype_numerical_answer_test extends advanced_testcase {
     public function test_within_tolerance_nominal() {
         $answer = new qtype_numerical_answer(13, 7.0, 1.0, '', FORMAT_MOODLE, 1.0);
@@ -38,16 +40,46 @@ class qtype_numerical_answer_test extends advanced_testcase {
         $this->assertFalse($answer->within_tolerance(8.01));
     }
 
+    public function test_within_tolerance_nominal_zero() {
+        // Either an answer or tolerance of 0 requires special care. We still
+        // don't want to end up comparing two floats for absolute equality.
+
+        // Zero tol, non-zero answer.
+        $answer = new qtype_numerical_answer(13, 1e-20, 1.0, '', FORMAT_MOODLE, 0.0);
+        $this->assertFalse($answer->within_tolerance(0.9999999e-20));
+        $this->assertTrue($answer->within_tolerance(1e-20));
+        $this->assertFalse($answer->within_tolerance(1.0000001e-20));
+
+        // Non-zero tol, zero answer.
+        $answer = new qtype_numerical_answer(13, 0.0, 1.0, '', FORMAT_MOODLE, 1e-24);
+        $this->assertFalse($answer->within_tolerance(-2e-24));
+        $this->assertTrue($answer->within_tolerance(-1e-24));
+        $this->assertTrue($answer->within_tolerance(0));
+        $this->assertTrue($answer->within_tolerance(1e-24));
+        $this->assertFalse($answer->within_tolerance(2e-24));
+
+        // Zero tol, zero answer.
+        $answer = new qtype_numerical_answer(13, 0.0, 1.0, '', FORMAT_MOODLE, 1e-24);
+        $this->assertFalse($answer->within_tolerance(-1e-20));
+        $this->assertTrue($answer->within_tolerance(-1e-35));
+        $this->assertTrue($answer->within_tolerance(0));
+        $this->assertTrue($answer->within_tolerance(1e-35));
+        $this->assertFalse($answer->within_tolerance(1e-20));
+
+        // Non-zero tol, non-zero answer.
+        $answer = new qtype_numerical_answer(13, 1e-20, 1.0, '', FORMAT_MOODLE, 1e-24);
+        $this->assertFalse($answer->within_tolerance(1.0002e-20));
+        $this->assertTrue($answer->within_tolerance(1.0001e-20));
+        $this->assertTrue($answer->within_tolerance(1e-20));
+        $this->assertTrue($answer->within_tolerance(1.0001e-20));
+        $this->assertFalse($answer->within_tolerance(1.0002e-20));
+    }
+
     public function test_within_tolerance_blank() {
         $answer = new qtype_numerical_answer(13, 1234, 1.0, '', FORMAT_MOODLE, '');
         $this->assertTrue($answer->within_tolerance(1234));
         $this->assertFalse($answer->within_tolerance(1234.000001));
         $this->assertFalse($answer->within_tolerance(0));
-
-        $answer = new qtype_numerical_answer(13, 0, 1.0, '', FORMAT_MOODLE, '');
-        $this->assertTrue($answer->within_tolerance(0));
-        $this->assertFalse($answer->within_tolerance(pow(10, -1 * ini_get('precision') + 1)));
-        $this->assertTrue($answer->within_tolerance(pow(10, -1 * ini_get('precision'))));
     }
 
     public function test_within_tolerance_relative() {