However, this multiplication is essentially adding 1.234 to itself 9 times such as 1.234 + 1.234 + … + 1.234 so the rounding guideline for addition and subtraction described below is more proper rounding approach. As a result, the final answer is 1.234 + 1.234 + … + 1.234 = 11.10 = 11.106 (one significant digit increase). Addition and subtraction For quantities created from measured quantities via addition and subtraction, the last significant figure position (e.g., hundreds, tens, ones, tenths, hundredths, and so forth) in the calculated result should be the same as the leftmost or largest digit position among the last significant figures of the measured quantities in the calculation. For example, 1.234 + 2 = .234 ≈ 3 1.234 + 2.0 = 3.34 ≈ 3.2 0.01234 + 2 = .01234 ≈ 2 with the last significant figures in the ones place, tenths place, and ones place respectively. (2 here is assumed not an exact number.) For the first example, the first term has its last significant figure in the thousandths place and the second term has its last significant figure in the ones place. The leftmost or largest digit position among the last significant figures of these terms is the ones place, so the calculated result should also have its last significant figure in the ones place. The rule to calculate significant figures for multiplication and division are not the same as the rule for addition and subtraction. For multiplication and division, only the total number of significant figures in each of the factors in the calculation matters; the digit position of the last significant figure in each factor is irrelevant. For addition and subtraction, only the digit position of the last significant figure in each of the terms in the calculation matters; the total number of significant figures in each term is irrelevant. However, greater accuracy will often be obtained if some non-significant digits are maintained in intermediate results which are used in subsequent calculations. Logarithm and antilogarithm The base-10 logarithm of a normalized number (i.e., a × 10b with 1 ≤ a < 10 and b as an integer), is rounded such that its decimal part (called mantissa) has as many significant figures as the significant figures in the normalized number. log10(3.000 × 104) = log10(104) + log10(3.000) = 4.000000... (exact number so infinite significant digits) + 0.477212547... = 4.477212547 ≈ 4.4771. When taking the antilogarithm