term has two digits of significance, the sum carried over into the tens columns so the answer has three digits of significance. 100 + 110 ≈ 200 We see the answer is 200, given the significance to the hundreds place of the 100. The answer maintains a single digit of significance in the hundreds place, just like the first term in the arithmetic. 100. + 110. = 210. 100. and 110. are both significant to the ones place (as indicated by the decimal), so the answer is also significant to the ones place. 1 × 102 + 1.1 × 102 ≈ 2 × 102 100 is significant up to the hundreds place, while 110 is up to the tens place. Of the two, the least accurate is the hundreds place. The answer should not have significant digits past the hundreds place. 1.0 × 102 + 111 = 2.1 × 102 1.0 × 102 is significant up to the tens place while 111 has numbers up until the ones place. The answer will have no significant figures past the tens place. 123.25 + 46.0 + 86.26 ≈ 255.5 123.25 and 86.26 are significant until the hundredths place while 46.0 is only significant until the tenths place. The answer will be significant up until the tenths place. 100 − 1 ≈ 100 We see the answer is 100, given the significance to the hundredths place of the 100. It may seem counter-intuitive, but giving the nature of significant digits dictating precision, we can see how this follows from the standard rules. Transcendental functions Transcendental functions have a complicated method to determine the significance of the function output. These include logarithmic functions, exponential functions and the trigonometric functions. The significance of the output depends on the condition number. In general, the number of significant figures of the output is equal to the number of significant figures of the function input (function argument) minus the order of magnitude of the condition number. The condition number of a differentiable function at a point is see Condition number: One variable for details. Note that if a function has a zero at a point, its condition number at the point is infinite, as infinitesimal changes in the input can change the output from zero to non-zero, yielding a ratio with zero in the denominator, hence an infinite relative change. The condition number of the most used functions