Conventions for Rounding and Significant Figures

DOE-STD-1121-98

2.5 CONVENTIONS FOR ROUNDING AND SIGNIFICANT FIGURES

The need to distinguish between exact numbers, such as dose limits, and imprecise numbers, such as

the results of measurements, leads to the use of some conventions in this DOE Standard.

Any legislated number, as well as any integer or ratio of two integers, is an exact number with no

uncertainty1. Examples of exact numbers are the 5-rem annual TEDE limit, the DAC for radon progeny

of 1/3 WL, and integral fractions and exponents (e.g., kinetic energy = 1/2 mv2). Exact numbers may

have tolerances, but when tolerances are not specified, the exact numbers must be treated as arbitrarily

precise: a 5-rem limit is 5.000 000 000 rems.

Measurements are often uncertain and imprecise, and inferences of dose from measurements using

calculational models with uncertain parameters are also uncertain and imprecise. Confusion sometimes

results when comparing uncertain or imprecise numbers with exact standards. Furthermore, difficulty

arises when exact numbers are converted from one set of units to another and the result is rounded. This

difficulty becomes particularly acute for quantities and units associated with radon and thoron. Thus, the

DOE has decided to derive all radon and thoron concentration values from 10 CFR 835, Appendix A,

PAEC limits (or ICRP/IAEA PAEE limits for newer recommendations), rather than from 10 CFR 835,

Appendix A, equilibrium equivalent DACs, which give slightly different answers and lead to confusion

(Strom et al. 1996).

Excellent, detailed guidance on significant figures and rounding for measurements is given by the

ASTM (ASTM 1993). Unfortunately, ASTM E380-93 does not recognize the exact nature of regulatory

limits nor address the problems of significant figures when converting exact numbers between unit

systems. Also, it does not address radon and thoron quantities and units.

To minimize roundoff errors, it is recommended that all calculations be performed using numbers

specified to at least "single precision" (six to seven significant figures) or as rational numbers if

appropriate (ratios of integers, e.g., 1/3, 5/12, etc.) For reporting purposes, it should be acceptable to

round to three significant figures or to the precision of the reporting field, whichever is less. For example,

3.84 mrem may be rounded to 4 mrem if only integral numbers of mrem can be reported in a given field.

More detail on recording and reporting is given in Section 9.

Similarly, in this DOE Standard, all numbers that are simply unit conversions are expressed to 5

significant figures to prevent contradictions or inconsistencies.

Some irrational numbers are exact, such as B, o2, and e, the base of the natural logarithms.

Sometimes, unit conversions are exact, such as 37,000,000,000 Bq/Ci.