diff --git a/src/Parser.php b/src/Parser.php
index 269175b..531fe69 100644
--- a/src/Parser.php
+++ b/src/Parser.php
@@ -40,11 +40,45 @@ public function extractValue(): string
 
         [$digits, $decimals] = array_pad(explode('.', $matches[1]), 2, '0');
 
-        $decimals = substr(strval(round(floatval('0.' . $decimals), 2)), 2);
+        $negative = str_starts_with($digits, '-');
+        $whole = ltrim($digits, '-');
+        if($whole === '') {
+            $whole = '0';
+        }
+
+        $rounded = number_format(round(floatval('0.' . $decimals), 2), 2, '.', '');
+        [$carry, $cents] = explode('.', $rounded);
+        if($carry === '1') {
+            $whole = $this->increment($whole);
+        }
+
+        $value = ltrim($whole . $cents, '0');
+        if($value === '') {
+            $value = '0';
+        }
+        if($negative && $value !== '0') {
+            $value = '-' . $value;
+        }
 
-        $value = ltrim($digits . str_pad($decimals, 2, '0'), '0');
+        return $value;
+    }
+
+    /**
+     * Add one to a whole-unit digit string.
+     */
+    protected function increment(string $whole): string
+    {
+        $chars = str_split($whole);
+        for($i = count($chars) - 1; $i >= 0; $i--) {
+            if($chars[$i] !== '9') {
+                $chars[$i] = (string) ((int) $chars[$i] + 1);
+
+                return implode('', $chars);
+            }
+            $chars[$i] = '0';
+        }
 
-        return strlen($value) ? $value : '0';
+        return '1' . implode('', $chars);
     }
 
     /**
diff --git a/tests/Unit/ParsesMonetaryStringsTest.php b/tests/Unit/ParsesMonetaryStringsTest.php
index f1627d3..3692c57 100644
--- a/tests/Unit/ParsesMonetaryStringsTest.php
+++ b/tests/Unit/ParsesMonetaryStringsTest.php
@@ -37,6 +37,14 @@
     expect(Price::parse('bar 6.50', 'EUR')->__toString())->toBe('EUR 6.50');
 });
 
+it('keeps a rounded cent that carries into the next unit', function() {
+    expect(Price::parse('1.999', 'EUR')->__toString())->toBe('EUR 2.00');
+    expect(Price::parse('0.999', 'EUR')->__toString())->toBe('EUR 1.00');
+    expect(Price::parse('4.995', 'EUR')->__toString())->toBe('EUR 5.00');
+    expect(Price::parse('-1.999', 'EUR')->__toString())->toBe('EUR -2.00');
+    expect(Price::parse('9.996', 'EUR')->__toString())->toBe('EUR 10.00');
+});
+
 it('parses values with both narrow non-breaking and regular spaces', function() {
     expect(Price::parse('1 234,56', 'EUR')->__toString())->toBe('EUR 1234.56');
     expect(Price::parse('1 234,56', 'EUR')->__toString())->toBe('EUR 1234.56');