BigDecimal, precision and scale

Java Problem Overview

I'm using BigDecimal for my numbers in my application, for example, with JPA. I did a bit of researching about the terms 'precision' and 'scale' but I don't understand what are they exactly.

Can anyone explain me the meaning of 'precision' and 'scale' for a BigDecimal value?

@Column(precision = 11, scale = 2)

Thanks!

Java Solutions

Solution 1 - Java

A BigDecimal is defined by two values: an arbitrary precision integer and a 32-bit integer scale. The value of the BigDecimal is defined to be $unscaledValue*10^{-scale}$ .

Precision: > The precision is the number of digits in the unscaled value. For instance, for the number 123.45, the precision returned is 5.

So, precision indicates the length of the arbitrary precision integer. Here are a few examples of numbers with the same scale, but different precision:

12345 / 100000 = 0.12345 // scale = 5, precision = 5
12340 / 100000 = 0.1234 // scale = 5, precision = 4
1 / 100000 = 0.00001 // scale = 5, precision = 1

In the special case that the number is equal to zero (i.e. 0.000), the precision is always 1.

Scale: > If zero or positive, the scale is the number of digits to the right of the decimal point. If negative, the unscaled value of the number is multiplied by ten to the power of the negation of the scale. For example, a scale of -3 means the unscaled value is multiplied by 1000.

This means that the integer value of the ‘BigDecimal’ is multiplied by $10^{-scale}$ .

Here are a few examples of the same precision, with different scales:

12345 with scale 5 = 0.12345
12345 with scale 4 = 1.2345
…
12345 with scale 0 = 12345
12345 with scale -1 = 123450 †

BigDecimal.toString:

The toString method for a BigDecimal behaves differently based on the scale and precision. (Thanks to @RudyVelthuis for pointing this out.)

If scale == 0, the integer is just printed out, as-is.
If scale < 0, E-Notation is always used (e.g. 5 scale -1 produces "5E+1")
If scale >= 0 and precision - scale -1 >= -6 a plain decimal number is produced (e.g. 10000000 scale 1 produces "1000000.0")
Otherwise, E-notation is used, e.g. 10 scale 8 produces "1.0E-7" since precision - scale -1 equals $unscaledValue*10^{-scale}$ is less than -6.

More examples:

19/100 = 0.19 // integer=19, scale=2, precision=2
1/1000 = 0.0001 // integer=1, scale = 4, precision = 1

Solution 2 - Java

Precision: Total number of significant digits
Scale: Number of digits to the right of the decimal point

See BigDecimal class documentation for details.

Solution 3 - Java

Quoting Javadoc:

> The precision is the number of digits in the unscaled value.

and

> If zero or positive, the scale is the number of digits to the right of the decimal point. If negative, the unscaled value of the number is multiplied by ten to the power of the negation of the scale. For example, a scale of -3 means the unscaled value is multiplied by 1000.

Solution 4 - Java

From your example annotation the maximum digits is 2 after the decimal point and 9 before (totally 11): 123456789,01

Solution 5 - Java

Precision is the total number of significant digits in a number. Scale is the number of digits to the right of the decimal point.

Examples:

123.456 Precision=6 Scale=3

10 Precision=2 Scale=0

-96.9923 Precision=6 Scale=4

0.0 Precision=1 Scale=1

Negative Scale

For a negative scale value, we apply the following formula: result = (given number) * 10 ^ (-(scale value)) Example

Given number = 1234.56

scale = -5

-> (1234.56) * 10^(-(-5))

-> (1234.56) * 10^(+5)

-> 123456000

Reference: https://www.logicbig.com/quick-info/programming/precision-and-scale.html

Content Type	Original Author	Original Content on Stackoverflow
Question	jpadilladev	View Question on Stackoverflow
Solution 1 - Java	Austin	View Answer on Stackoverflow
Solution 2 - Java	hamena314	View Answer on Stackoverflow
Solution 3 - Java	Andy Turner	View Answer on Stackoverflow
Solution 4 - Java	adranale	View Answer on Stackoverflow
Solution 5 - Java	Shadyar	View Answer on Stackoverflow