# 1.14. Select a method to eliminate rounding errors which is suitable for the purpose of the document

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A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value. Numerical analysis specifically tries to estimate this error when using approximation equations and/or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits). This is a form of quantisation error.

When a sequence of calculations subject to rounding error is made, errors may accumulate, sometimes dominating the calculation. Cases where significant error accumulates are known as ill-conditioned

Increasing the number of digits allowed in a representation reduces the magnitude of possible round-off errors, but any representation limited to finitely many digits will still cause some degree of round-off error for uncountable many real numbers. Additional digits used for intermediary steps of a calculation are known as guard digits.

There are some standard ways of performing the rounding in arithmetic. Select a method to eliminate rounding errors which is suitable for the purpose of the document:

- Truncation: Keep the desired number of digits unchanged, removing all less-significant digits; also called rounding toward zero. 0.142857 ≈ 0.142 (All digits less significant than the third removed)
- Round to Nearest: Round to the nearest valid representation. Break ties by rounding either to an even digit (default), or away from zero.
- Round to −∞: Round to a value less than or equal to the original number. If the original number is positive, this is equivalent to truncation.
- Round to +∞: Round to a value greater than or equal to the original number. If the original number is negative, this is equivalent to truncation.

Breaking ties by rounding towards an even value preserves the expected value of the original number and treats positive and negative numbers symmetrically, and also slightly more often supplies an even number that is less likely than an odd number to cause a rounding decision in later computations if those are similar to the computation that resulted in falling at just that mid-point (e.g., if it is being fed back into an iteration). It is common practice in meteorology to round published temperatures towards an odd value in such situations; this has all the same properties apart from the last.

Select the method most likely to eliminate rounding errors for you Information System.

**Keep confidential information secure and do not disclose it to unauthorised people**

Application owners must ensure that only users with a specific business reason to access an application can access that application and no more than that application. They must keep confidential information secure and not disclose it to unauthorised people. Access rights to applications that can access confidential information must reflect a user’s current organisational status.

Administrative access rights to servers with confidential information must be limited to system administrators with a specific business reason for access and such access must be logged; any access rights must change if their organisation or status changes.

Access to non-electronic records containing confidential information must be restricted to people with a business need to access the records.

There must be written policies for employees that take into account whether and how employees should be allowed to keep access and transport records containing high risk confidential information about people other than themselves outside of business premises.