1. Conversions and Roundings Geert Temmerman National Bank of Belgium June 2007

2. Content • Conversions and roundings • Recommendations

3. Conversions and roundings • Document issued in November 1997 by General Commission for the euro: • 10 recommendations for general use (private sector, public administrations, ...) • based on European Council Regulation 1103/97 of 17.VI.1997 • Remark: 1 EUR = 40.3399 BEF • decimals of BEF passed out of use in most applications • EUR with 2 decimal places is same order of magnitude as BEF although allowing somewhat higher precision since 0.01 EUR = 0.40 BEF

4. Recommendation 1 Since most prices in BEF are expressed inunits of BEF, prices in EUR would normally be expressed with 2 decimal places.

5. Recommendation 2 • For (unit) prices expressed with higher than normal precision in BEF (= using decimal places for BEF price), the same precision should be maintained for EUR price : as a rule 2 more decimal places for EUR price than for BEF price. • e.g. • 1 screw : 0.35 BEF  0.0087 EUR • 1 megajoule gas : 0.22911 BEF  0.0056795 EUR • 1 litre Super+95 : 38.1 BEF  0.944 EUR

6. Recommendation 3 • Amounts to be paid or recorded in accounting: after conversion from EUR to BEF to be rounded off to nearest unity. • < .50: rounding down •  .50: rounding up • (Inversely no problem since EUR with 2 decimal places allows higher precision than BEF.)

7. Recommendation 4 Crossed conversions (from a national currency to another national currency via EUR) using computers or calculators: use highest possible precision for intermediary result.

8. Recommendation 5 Reconstitution of amount in EUR after having been converted to BEF (EUR BEF EUR): loss of precision of ± 0.01 EUR can not be avoided and has to be tolerated. This tolerance has to be integrated in computer applications. (Inversely, BEFEURBEF, no problem since EUR with 2 decimal places allows higher precision than BEF.)

9. Recommendation 6 During the 3 years transitional period, it is recommended to initiate payment in same currency (EUR or BEF) in which the amount to be paid is expressed on the invoice or the cash register receipt, in order to minimise effect of loss of precision (cf. recommendation 5).

10. Recommendation 7 • When elements of a mathematical operation (such as a sum) are converted and rounded off individually, it is as a rule recommended that the result is converted and rounded off also, instead of making the mathematical operation (sum) on the converted elements.e.g. BEFEUR • 1 246 30.89 1 754 43.48 473 11.73 427 10.59 813 20.15 398 9.87 126.71 5 111 126.70

11. Recommendation 8 There can however be reasons to act in the way opposite to recommendation 7, certainly when the individual elements are obviously more important than the result of the operation (sum), e.g. in statistical series. (Adopted by Tax Administration for conversion of individual entries in tax declaration.)

12. Recommendation 9 Limits in (continuous) scales are ordinarily mathematically converted into EUR and rounded off. e.g. BEF scalenew EUR scale x  500 x  12.39 500 < x  1000 12.39 < x  24.79 1000 < x  2000 24.79 < x  49.58 2000 < x  3000 49.58 < x  123.95 etc. etc.

13. Recommendation 9 However, limits in discrete scales can cause problems : gaps between limits may appear. In that case it is recommended to use as the lower limit of a parcel the higher limit of the underlying parcel plus 0.01 EUR, in order to avoid gaps. e.g. BEF scalemathematically into EURnew EUR scale from 0 to 500 from 0 to 12.39 from 0 to 12.39 from 501 to 1 000 from 12.42 to 24.79 from 12.40 to 24.79 from 1 001 to 2 000 from 24.81 to 49.58 from 24.80 to 49.58 from 2 001 to 5 000 from 49.60 to 123.95 from 49.59 to 123.95 etc. etc. etc.

14. Recommendation 10 Since small differences are unavoidable when converting and rounding off amounts, and differences of 0.01 EUR have to be tolerated (cf. recommendation 5), the Belgian Accounting Standards Board issued a recommendation to enter all differences as benefits or losses on dedicated sub-accounts of the financial results accounts of the Minimum Standard Chart of Accounts.