diff --git a/src/BigDecimal.php b/src/BigDecimal.php
index 74be2b7..a4deba1 100644
--- a/src/BigDecimal.php
+++ b/src/BigDecimal.php
@@ -48,6 +48,8 @@ final class BigDecimal extends BigNumber implements \Serializable
      * @param int                   $scale The scale of the number.
      *
      * @return BigDecimal
+     *
+     * @throws \InvalidArgumentException
      */
     public static function ofUnscaledValue($value, $scale = 0)
     {
diff --git a/src/BigNumber.php b/src/BigNumber.php
index e94777f..96b3105 100644
--- a/src/BigNumber.php
+++ b/src/BigNumber.php
@@ -3,6 +3,7 @@
 namespace Brick\Math;
 
 use Brick\Math\Exception\DivisionByZeroException;
+use Brick\Math\Exception\NumberFormatException;
 use Brick\Math\Exception\RoundingNecessaryException;
 
 /**
@@ -42,32 +43,26 @@ abstract class BigNumber
      *
      * @return static
      *
-     * @throws \InvalidArgumentException If the number is not valid.
-     * @throws DivisionByZeroException   If the value represents a rational number with a denominator of zero.
+     * @throws NumberFormatException      If the format of the number is not valid.
+     * @throws DivisionByZeroException    If the value represents a rational number with a denominator of zero.
      * @throws RoundingNecessaryException If the value represents a valid number, but this number cannot be converted
      *                                    to the subclass this method has been called on, without rounding.
      */
     public static function of($value)
     {
         if ($value instanceof BigNumber) {
-            try {
-                switch (static::class) {
-                    case BigInteger::class:
-                        return $value->toBigInteger();
+            switch (static::class) {
+                case BigInteger::class:
+                    return $value->toBigInteger();
 
-                    case BigDecimal::class:
-                        return $value->toBigDecimal();
+                case BigDecimal::class:
+                    return $value->toBigDecimal();
 
-                    case BigRational::class:
-                        return $value->toBigRational();
+                case BigRational::class:
+                    return $value->toBigRational();
 
-                    default:
-                        return $value;
-                }
-            } catch (RoundingNecessaryException $e) {
-                $className = substr(static::class, strrpos(static::class, '\\') + 1);
-
-                throw new \InvalidArgumentException('Cannot convert value to a ' . $className . ' without losing precision.');
+                default:
+                    return $value;
             }
         }
 
@@ -87,7 +82,7 @@ abstract class BigNumber
         $value = (string) $value;
 
         if (preg_match(BigNumber::REGEXP, $value, $matches) !== 1) {
-            throw new \InvalidArgumentException('The given value does not represent a valid number.');
+            throw new NumberFormatException('The given value does not represent a valid number.');
         }
 
         if (isset($matches['denominator'])) {
@@ -100,21 +95,15 @@ abstract class BigNumber
 
             $result = new BigRational(new BigInteger($numerator), new BigInteger($denominator), false);
 
-            try {
-                switch (static::class) {
-                    case BigInteger::class:
-                        return $result->toBigInteger();
+            switch (static::class) {
+                case BigInteger::class:
+                    return $result->toBigInteger();
 
-                    case BigDecimal::class:
-                        return $result->toBigDecimal();
+                case BigDecimal::class:
+                    return $result->toBigDecimal();
 
-                    default:
-                        return $result;
-                }
-            } catch (RoundingNecessaryException $e) {
-                $className = substr(static::class, strrpos(static::class, '\\') + 1);
-
-                throw new \InvalidArgumentException('Cannot convert value to a ' . $className . ' without losing precision.');
+                default:
+                    return $result;
             }
         } elseif (isset($matches['fractional']) || isset($matches['exponent'])) {
             $fractional = isset($matches['fractional']) ? $matches['fractional'] : '';
@@ -133,21 +122,15 @@ abstract class BigNumber
 
             $result = new BigDecimal($unscaledValue, $scale);
 
-            try {
-                switch (static::class) {
-                    case BigInteger::class:
-                        return $result->toBigInteger();
+            switch (static::class) {
+                case BigInteger::class:
+                    return $result->toBigInteger();
 
-                    case BigRational::class:
-                        return $result->toBigRational();
+                case BigRational::class:
+                    return $result->toBigRational();
 
-                    default:
-                        return $result;
-                }
-            } catch (RoundingNecessaryException $e) {
-                $className = substr(static::class, strrpos(static::class, '\\') + 1);
-
-                throw new \InvalidArgumentException('Cannot convert value to a ' . $className . ' without losing precision.');
+                default:
+                    return $result;
             }
         } else {
             $integral = BigNumber::cleanUp($matches['integral']);
diff --git a/src/Exception/NumberFormatException.php b/src/Exception/NumberFormatException.php
new file mode 100644
index 0000000..afc089e
--- /dev/null
+++ b/src/Exception/NumberFormatException.php
@@ -0,0 +1,11 @@
+<?php
+
+namespace Brick\Math\Exception;
+
+/**
+ * Exception thrown when attempting to create a number from a string with an invalid format.
+ */
+class NumberFormatException extends ArithmeticException
+{
+
+}
diff --git a/tests/BigDecimalTest.php b/tests/BigDecimalTest.php
index 2297384..1a4f6a5 100644
--- a/tests/BigDecimalTest.php
+++ b/tests/BigDecimalTest.php
@@ -163,7 +163,7 @@ class BigDecimalTest extends AbstractTestCase
 
     /**
      * @dataProvider providerOfInvalidValueThrowsException
-     * @expectedException \InvalidArgumentException
+     * @expectedException \Brick\Math\Exception\NumberFormatException
      *
      * @param string $value
      */
diff --git a/tests/BigIntegerTest.php b/tests/BigIntegerTest.php
index e0987b7..04f90eb 100644
--- a/tests/BigIntegerTest.php
+++ b/tests/BigIntegerTest.php
@@ -87,12 +87,12 @@ class BigIntegerTest extends AbstractTestCase
     }
 
     /**
-     * @dataProvider providerOfInvalidValueThrowsException
-     * @expectedException \InvalidArgumentException
+     * @dataProvider providerOfInvalidFormatThrowsException
+     * @expectedException \Brick\Math\Exception\NumberFormatException
      *
      * @param string|number $value
      */
-    public function testOfInvalidValueThrowsException($value)
+    public function testOfInvalidFormatThrowsException($value)
     {
         BigInteger::of($value);
     }
@@ -100,11 +100,9 @@ class BigIntegerTest extends AbstractTestCase
     /**
      * @return array
      */
-    public function providerOfInvalidValueThrowsException()
+    public function providerOfInvalidFormatThrowsException()
     {
         return [
-            [1.1],
-
             [''],
             ['a'],
             [' 1'],
@@ -113,7 +111,34 @@ class BigIntegerTest extends AbstractTestCase
             ['+'],
             ['-'],
             ['+a'],
-            ['-a']
+            ['-a'],
+            ['a0'],
+            ['0a'],
+            ['1.a'],
+            ['a.1'],
+        ];
+    }
+
+    /**
+     * @dataProvider providerOfNonConvertibleValueThrowsException
+     * @expectedException \Brick\Math\Exception\RoundingNecessaryException
+     *
+     * @param float|string $value
+     */
+    public function testOfNonConvertibleValueThrowsException($value)
+    {
+        BigInteger::of($value);
+    }
+
+    /**
+     * @return array
+     */
+    public function providerOfNonConvertibleValueThrowsException()
+    {
+        return [
+            [1.1],
+            ['1e-1'],
+            ['7/9'],
         ];
     }
 
diff --git a/tests/BigRationalTest.php b/tests/BigRationalTest.php
index 2b18570..8edc8a4 100644
--- a/tests/BigRationalTest.php
+++ b/tests/BigRationalTest.php
@@ -86,12 +86,12 @@ class BigRationalTest extends AbstractTestCase
     }
 
     /**
-     * @dataProvider providerParseInvalidString
-     * @expectedException \InvalidArgumentException
+     * @dataProvider providerOfInvalidString
+     * @expectedException \Brick\Math\Exception\NumberFormatException
      *
      * @param string $string An invalid string representation.
      */
-    public function testParseInvalidString($string)
+    public function testOfInvalidString($string)
     {
         BigRational::of($string);
     }
@@ -99,7 +99,7 @@ class BigRationalTest extends AbstractTestCase
     /**
      * @return array
      */
-    public function providerParseInvalidString()
+    public function providerOfInvalidString()
     {
         return [
             ['123/-456'],