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Understanding SQL Server Data Types: Approximate Numbers – REAL and FLOAT

Floating-point numbers in SQL Server, represented by the REAL and FLOAT data types, are designed to handle a wide range of numeric values with varying precision. Understanding their behavior is crucial for accurate data storage and retrieval, especially when dealing with numbers that have many digits or require dynamic decimal placement.

Understanding Approximate Numeric Data Types: REAL and FLOAT

SQL Server’s approximate numeric data types, REAL and FLOAT, are based on the IEEE 754 standard for floating-point arithmetic. This means they store approximate values rather than exact ones, making them suitable for scientific calculations, engineering data, or any scenario where precise decimal representation is less critical than the range of values or where the decimal point can “float.”

REAL (Single-Precision Floating-Point)

  • Storage: REAL data types use 4 bytes of storage.
  • Precision: They offer approximately 7 decimal digits of precision. This doesn’t mean they can only store numbers with 7 digits; rather, only about 7 digits are guaranteed to be accurate.
  • Equivalence: REAL is equivalent to FLOAT(24). You simply declare a column as REAL; there’s no need to specify REAL(n).

How REAL handles numbers:

The term “floating point” signifies that the decimal point is not fixed. It can “float” to different positions within the number, allowing REAL to represent both very small and very large numbers. For example, numbers like 1.234567, 123.4567, or 123456.7 can all be stored.

However, the key limitation lies in its precision. If you attempt to store a number with more than 7 significant digits, REAL will approximate it.

Example: Storing Pi in REAL

The value of Pi is 3.141592653589793. When you store this in a REAL column, it will be approximated to about 7 significant digits, typically 3.1415927. The subsequent digits are lost due to the limited precision.

Consider this scenario for REAL:

If you insert 1234567.89 into a REAL column:

  • This number has 9 total digits (7 before the decimal and 2 after).
  • Since REAL can only store about 7 significant digits precisely, SQL Server will round or truncate the value to fit within this precision.
  • The first 7 digits (1234567) are the most significant. The decimal part (.89) will likely be lost or rounded, resulting in a stored value close to 1234568.

If you insert 1234567890.1234567 into a REAL column:

  • This number has 10 digits before the decimal and 7 after, totaling 17 significant digits.
  • REAL can only handle approximately 7 significant digits.
  • SQL Server will approximate this to preserve the most significant digits. The stored value will be something like 1.234568E+09 (scientific notation), which represents 1,234,568,000. The decimal part and less significant digits are completely lost because even the integer part exceeds the 7-digit precision.

Important Note on REAL Behavior:

The REAL data type does not throw an error when you input a number with more digits than it can precisely handle. Instead, it silently stores an approximate version of your number, retaining about 7 significant digits. This behavior is crucial to understand as it can lead to data inaccuracies if not properly considered.

FLOAT (Double-Precision Floating-Point)

  • Storage: FLOAT data types can use either 4 bytes (when specified as FLOAT(24), making it equivalent to REAL) or 8 bytes.
  • Precision:
    • FLOAT(24) (4 bytes) offers approximately 7 decimal digits of precision (same as REAL).
    • FLOAT(53) (8 bytes, the default when you just use FLOAT without a precision) offers approximately 15-17 decimal digits of precision. This is why it can accommodate the full value of Pi (3.141592653589793).
  • Declaration: When you use FLOAT, you can optionally specify a precision n (e.g., FLOAT(n)).
    • If n is between 1 and 24, it’s treated as REAL (4 bytes).
    • If n is between 25 and 53, it’s treated as FLOAT (8 bytes).
    • If no n is specified (e.g., just FLOAT), it defaults to FLOAT(53).

Choosing Between REAL and FLOAT

  • REAL: Best for situations where a reasonable degree of precision (around 7 digits) is sufficient and storage space is a significant concern.
  • FLOAT (specifically FLOAT(53) or just FLOAT): Ideal when higher precision (15-17 digits) is required, such as in scientific calculations or when you need to store numbers like the full value of Pi without significant loss of precision.

Use Cases for REAL and FLOAT

Both REAL and FLOAT are well-suited for scenarios where:

  • Approximate values are acceptable: Scientific measurements, engineering calculations, and financial data where slight variations due to approximation are within tolerance.
  • Numbers have a wide range: They can handle very small and very large numbers without requiring a fixed decimal point.
  • Performance is a factor: Floating-point operations can sometimes be faster than exact decimal arithmetic, especially for complex calculations.

Example in a Supply Chain System:

Consider a supply chain system that needs to store various numeric values, such as weights, dimensions, or sensor readings.

  • 1234567
  • 12.34567
  • 1.234567
  • 123456.7
  • 123.4567
  • 12345.67

These numbers demonstrate a “floating” decimal point and varying total digits. While DECIMAL or NUMERIC could accommodate these if their maximum precision and scale were carefully defined, REAL often presents a simpler and more flexible choice for such diverse approximate numbers, provided the 7-digit precision is acceptable. If higher precision is occasionally needed, FLOAT (8-byte) would be the better choice.

When to avoid REAL and FLOAT:

  • Exact Decimal Precision is Critical: For financial transactions, monetary values, or any data where even the smallest deviation is unacceptable, always use DECIMAL or NUMERIC. These data types store exact decimal values.
  • Comparisons for Equality: Due to their approximate nature, directly comparing REAL or FLOAT values for exact equality (=) can lead to unexpected results. Instead, compare if the difference between two floating-point numbers is within a small tolerance.

In conclusion, REAL and FLOAT are powerful data types for handling approximate numeric values in SQL Server. By understanding their precision limitations and use cases, you can effectively choose the right data type to ensure data integrity and optimize performance in your database designs.