of a normalized number, the result is rounded to have as many significant figures as the significant figures in the decimal part of the number to be antiloged. 104.4771 = 2998.5318119... = 30000 = 3.000 × 104. Transcendental functions If a transcendental function (e.g., the exponential function, the logarithm, and the trigonometric functions) is differentiable at its domain element x, then its number of significant figures (denoted as "significant figures of ") is approximately related with the number of significant figures in x (denoted as "significant figures of x") by the formula , where is the condition number. See the significance arithmetic article to find its derivation. Round only on the final calculation result When performing multiple stage calculations, do not round intermediate stage calculation results; keep as many digits as is practical (at least one more digit than the rounding rule allows per stage) until the end of all the calculations to avoid cumulative rounding errors while tracking or recording the significant figures in each intermediate result. Then, round the final result, for example, to the fewest number of significant figures (for multiplication or division) or leftmost last significant digit position (for addition or subtraction) among the inputs in the final calculation. (2.3494 + 1.345) × 1.2 = 3.694 × 1.2 = 4.3328 ≈ 4.4. (2.3494 × 1.345) + 1.2 = 3.15943 + 1.2 = 4.59943 ≈ 4.4. Estimating an extra digit When using a ruler, initially use the smallest mark as the first estimated digit. For example, if a ruler's smallest mark is 0.1 cm, and 4.5 cm is read, then it is 4.5 (±0.1 cm) or 4.4 cm to 4.6 cm as to the smallest mark interval. However, in practice a measurement can usually be estimated by eye to closer than the interval between the ruler's smallest mark, e.g. in the above case it might be estimated as between 4.51 cm and 4.53 cm. It is also possible that the overall length of a ruler may not be accurate to the degree of the smallest mark, and the marks may be imperfectly spaced within each unit. However assuming a normal good quality ruler, it should be possible to estimate tenths between the nearest two marks to achieve an extra decimal place of accuracy. Failing to do this adds the error in reading the ruler to any error in the calibration of the ruler. Estimation in statistic When