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BigDecimal, precision and scale

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!

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jpadilladev Avatar asked Feb 16 '16 14:02

jpadilladev


People also ask

What is scale and precision in BigDecimal?

A BigDecimal consists of an arbitrary precision integer unscaled value and a 32-bit integer 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.

What does precision mean in BigDecimal?

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

How accurate is BigDecimal?

This limits it to 15 to 17 decimal digits of accuracy. BigDecimal can grow to any size you need it to. Double operates in binary which means it can only precisely represent numbers which can be expressed as a finite number in binary. For example, 0.375 in binary is exactly 0.011.


2 Answers

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
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Austin Avatar answered Sep 29 '22 18:09

Austin


  • Precision: Total number of significant digits

  • Scale: Number of digits to the right of the decimal point

See BigDecimal class documentation for details.

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hamena314 Avatar answered Sep 29 '22 17:09

hamena314