# Using Rationals to avoid rounding errors in calculations

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Ruby has the class which allows you to store exact fractions. Any calculation on these variables will now use fractional calculations internally, until you convert the result to another data type or do a calculation which requires an implicit conversion.

## Example use case:

Lets say you want to store the conversion factor from `MJ` to `kWh` in a variable, which is `1/3.6`. Using BigDecimals for this seems like a good idea, it usually helps with rounding errors over a float, but there are cases where you still have to worry about rounding errors.

``````conversion_factor = BigDecimal('1') / BigDecimal('3.6')
# => 0.277777777777777777777777777777777778e0
``````

Here the conversion factor got rounded after some decimal places. If you now use this value now to convert a Value from `MJ` to `kWh` it can lead to ugly rounding errors.

``````BigDecimal('7.2') * conversion_factor
# => 0.20000000000000000000000000000000000016e1
``````

This might be OK for you as the value is still very accurate. When you later round the value, e.g. for displaying it might not be an issue, but can be annoying to deal with during development and in tests.

### To avoid this use Rationals

``````conversion_factor = Rational('1') / Rational('3.6')
# => (5/18)
result = Rational('7.2') * conversion_factor
# => (2/1)
result.to_d(0)
# => 0.2e1
``````

#### Note

The `0` in `result.to_d(0)` is the , which is applied to the `BigDecimal` return value.

## Using Rationals has some pitfalls you should be aware of:

• Multiplying a Rational with a BigDecimal still produces rounding errors.

``````BigDecimal('7.2') * (Rational('1') / Rational('3.6'))
# => 0.20000000000000000016e1
``````
• Rationals don't like floats very much, when initializing a Rational with a float you don't get accurate values.

``````float_rational = Rational(0.1)
# => (3602879701896397/36028797018963968)
float_rational.to_d(0)
# => 0.100000000000000005551115123125782702e0
``````
Martin Schaflitzl
Last edit
Felix Eschey