diff --git a/lib/parse.js b/lib/parse.js
index 84d142f..af5556b 100644
--- a/lib/parse.js
+++ b/lib/parse.js
@@ -206,21 +206,29 @@ var json_parse = function (options) {
         error('Bad number');
       } else {
         if (BigNumber == null) BigNumber = require('bignumber.js');
-        if (Number.isSafeInteger(number))
-          return !_options.alwaysParseAsBig
-            ? number
-            : _options.useNativeBigInt
-            ? BigInt(number)
-            : new BigNumber(number);
-        else
-          // Number with fractional part should be treated as number(double) including big integers in scientific notation, i.e 1.79e+308
-          return _options.storeAsString
-            ? string
-            : /[\.eE]/.test(string)
-            ? number
-            : _options.useNativeBigInt
-            ? BigInt(string)
-            : new BigNumber(string);
+
+        if (Number.isSafeInteger(number)) {
+          return _options.alwaysParseAsBig 
+            ? (_options.useNativeBigInt ? BigInt(number) : new BigNumber(number))
+            : number;
+        }
+
+        // If the number has a decimal or exponential part, it can't be
+        // represented as BigInt, not always.
+        if (/[\.eE]/.test(string)) {
+          if (_options.storeAsString) {
+            const exponent = Math.floor(Math.log2(Math.abs(number)));
+            if (exponent > 53) {
+              return string;
+            }
+          }
+          return number;
+        }
+
+        // Remaining cases: large integers
+        return _options.storeAsString
+          ? string
+          : (_options.useNativeBigInt ? BigInt(string) : new BigNumber(string));
       }
     },
     string = function () {
diff --git a/test/bigint-parse-test.js b/test/bigint-parse-test.js
index 4156b3e..c97f71f 100644
--- a/test/bigint-parse-test.js
+++ b/test/bigint-parse-test.js
@@ -71,4 +71,26 @@ describe("Testing native BigInt support: parse", function () {
     expect(output).to.equal(input);
     done();
   });
+
+  it("Should show JSONbig parses decimal numbers as numbers, not strings", function (done) {
+    var JSONbig = require('../index')({
+      "storeAsString": true
+    });
+    var input = '{"testNumber": 95.45454545454545}';
+    var obj = JSONbig.parse(input);
+    expect(obj.testNumber.toString(), "test number").to.equal("95.45454545454545");
+    expect(typeof obj.testNumber, "test number").to.equal('number');
+    done();
+  });
+
+  it("Should show JSONbig parses large decimal numbers as strings when storeAsString is true", function (done) {
+    var JSONbig = require('../index')({
+      "storeAsString": true
+    });
+    var input = '{"largeDecimal": 100000000000000000001.23}';
+    var obj = JSONbig.parse(input);
+    expect(obj.largeDecimal, "large decimal number").to.equal("100000000000000000001.23");
+    expect(typeof obj.largeDecimal, "large decimal number").to.equal('string');
+    done();
+  });
 });
\ No newline at end of file