diff --git a/build/types/core b/build/types/core
index 23d04a5c8f..5f322c0e7d 100644
--- a/build/types/core
+++ b/build/types/core
@@ -105,6 +105,7 @@
 +../../lib/util/multi_map.js
 +../../lib/util/mutex.js
 +../../lib/util/networking.js
++../../lib/util/number_utils.js
 +../../lib/util/object_utils.js
 +../../lib/util/operation_manager.js
 +../../lib/util/periods.js
diff --git a/lib/player.js b/lib/player.js
index 4639cbf2ad..cf465f4bde 100644
--- a/lib/player.js
+++ b/lib/player.js
@@ -56,6 +56,7 @@ goog.require('shaka.util.ManifestParserUtils');
 goog.require('shaka.util.MediaReadyState');
 goog.require('shaka.util.MimeUtils');
 goog.require('shaka.util.Mutex');
+goog.require('shaka.util.NumberUtils');
 goog.require('shaka.util.ObjectUtils');
 goog.require('shaka.util.Platform');
 goog.require('shaka.util.PlayerConfiguration');
@@ -705,7 +706,7 @@ shaka.Player = class extends shaka.util.FakeEventTarget {
     this.externalSrcEqualsThumbnailsStreams_ = [];
 
     /** @private {number} */
-    this.completionPercent_ = NaN;
+    this.completionPercent_ = -1;
 
     /** @private {?shaka.extern.PlayerConfiguration} */
     this.config_ = this.defaultConfig_();
@@ -1457,7 +1458,7 @@ shaka.Player = class extends shaka.util.FakeEventTarget {
 
       this.externalSrcEqualsThumbnailsStreams_ = [];
 
-      this.completionPercent_ = NaN;
+      this.completionPercent_ = -1;
 
       // Make sure that the app knows of the new buffering state.
       this.updateBufferState_();
@@ -6370,41 +6371,46 @@ shaka.Player = class extends shaka.util.FakeEventTarget {
     if (!this.video_) {
       return;
     }
-    let hasNewCompletionPercent = false;
-    const completionRatio = this.video_.currentTime / this.video_.duration;
-    if (!isNaN(completionRatio)) {
-      const percent = Math.round(100 * completionRatio);
-      if (isNaN(this.completionPercent_)) {
-        this.completionPercent_ = percent;
-        hasNewCompletionPercent = true;
-      } else {
-        const newCompletionPercent = Math.max(this.completionPercent_, percent);
-        if (this.completionPercent_ != newCompletionPercent) {
-          this.completionPercent_ = newCompletionPercent;
-          hasNewCompletionPercent = true;
-        }
+
+    const isQuartile = (quartilePercent, currentPercent) => {
+      const NumberUtils = shaka.util.NumberUtils;
+
+      if ((NumberUtils.isFloatEqual(quartilePercent, currentPercent) ||
+          currentPercent > quartilePercent) &&
+          this.completionPercent_ < quartilePercent) {
+        this.completionPercent_ = quartilePercent;
+        return true;
       }
+      return false;
+    };
+
+    const completionRatio = this.video_.currentTime / this.video_.duration;
+
+    if (isNaN(completionRatio)) {
+      return;
     }
-    if (hasNewCompletionPercent) {
-      let event;
-      if (this.completionPercent_ == 0) {
-        event = shaka.Player.makeEvent_(shaka.util.FakeEvent.EventName.Started);
-      } else if (this.completionPercent_ == 25) {
-        event = shaka.Player.makeEvent_(
-            shaka.util.FakeEvent.EventName.FirstQuartile);
-      } else if (this.completionPercent_ == 50) {
-        event = shaka.Player.makeEvent_(
-            shaka.util.FakeEvent.EventName.Midpoint);
-      } else if (this.completionPercent_ == 75) {
-        event = shaka.Player.makeEvent_(
-            shaka.util.FakeEvent.EventName.ThirdQuartile);
-      } else if (this.completionPercent_ == 100) {
-        event = shaka.Player.makeEvent_(
-            shaka.util.FakeEvent.EventName.Complete);
-      }
-      if (event) {
-        this.dispatchEvent(event);
-      }
+
+    const percent = completionRatio * 100;
+
+    let event;
+    if (isQuartile(0, percent)) {
+      event = shaka.Player.makeEvent_(shaka.util.FakeEvent.EventName.Started);
+    } else if (isQuartile(25, percent)) {
+      event = shaka.Player.makeEvent_(
+          shaka.util.FakeEvent.EventName.FirstQuartile);
+    } else if (isQuartile(50, percent)) {
+      event = shaka.Player.makeEvent_(
+          shaka.util.FakeEvent.EventName.Midpoint);
+    } else if (isQuartile(75, percent)) {
+      event = shaka.Player.makeEvent_(
+          shaka.util.FakeEvent.EventName.ThirdQuartile);
+    } else if (isQuartile(100, percent)) {
+      event = shaka.Player.makeEvent_(
+          shaka.util.FakeEvent.EventName.Complete);
+    }
+
+    if (event) {
+      this.dispatchEvent(event);
     }
   }
 
diff --git a/lib/util/number_utils.js b/lib/util/number_utils.js
new file mode 100644
index 0000000000..f3aa3e37c7
--- /dev/null
+++ b/lib/util/number_utils.js
@@ -0,0 +1,37 @@
+/*! @license
+ * Shaka Player
+ * Copyright 2016 Google LLC
+ * SPDX-License-Identifier: Apache-2.0
+ */
+
+goog.provide('shaka.util.NumberUtils');
+
+
+shaka.util.NumberUtils = class {
+  /**
+   * Compare two float numbers, taking a configurable tolerance margin into
+   * account.
+   *
+   * @param {number} a
+   * @param {number} b
+   * @param {number=} tolerance
+   * @return {boolean}
+   */
+  static isFloatEqual(a, b, tolerance = Number.EPSILON) {
+    if (a === b) {
+      return true;
+    }
+
+    const error = Math.abs(a - b);
+
+    if (error <= tolerance) {
+      return true;
+    }
+
+    if (tolerance !== Number.EPSILON) {
+      return Math.abs(error - tolerance) <= Number.EPSILON;
+    }
+
+    return false;
+  }
+};
diff --git a/test/util/number_utils_unit.js b/test/util/number_utils_unit.js
new file mode 100644
index 0000000000..647dfa3383
--- /dev/null
+++ b/test/util/number_utils_unit.js
@@ -0,0 +1,20 @@
+/*! @license
+ * Shaka Player
+ * Copyright 2016 Google LLC
+ * SPDX-License-Identifier: Apache-2.0
+ */
+
+describe('NumberUtils', () => {
+  const NumberUtils = shaka.util.NumberUtils;
+
+  it('compares float', () => {
+    expect(NumberUtils.isFloatEqual(0.1 + 0.2, 0.3)).toBe(true);
+    expect(NumberUtils.isFloatEqual(0.4 - 0.1, 0.3)).toBe(true);
+    expect(NumberUtils.isFloatEqual(0.0004, 0.0003)).toBe(false);
+  });
+
+  it('respects provided tolerance margin', () => {
+    expect(NumberUtils.isFloatEqual(1.5, 1.4)).toBe(false);
+    expect(NumberUtils.isFloatEqual(1.5, 1.4, 0.1)).toBe(true);
+  });
+});