Arithmetic
An approximate rule of thumb often used when performing calculations by hand is as follows.
For multiplication and division, the result should have as many significant figures as the measured number with the smallest number of significant figures.
For addition and subtraction, the result should have as many decimal places as the measured number with the smallest number of decimal places (for example, 100.0 + 1.111 = 101.1).
In a logarithm, the numbers to the right of the decimal point are called the mantissa and the number of significant figures must be the same as the number of digits in the mantissa (for example, log(3.000×104) = 4.47712125472, should be rounded to 4.4771).
When taking antilogarithms, the resulting number should have as many significant figures as the mantissa in the logarithm.
When performing a calculation, do not follow these guidelines for intermediate results; keep as many digits as is practical until the end of calculation to avoid rounding errors.
Read more about this topic: Significant Figures
Famous quotes containing the word arithmetic:
“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”
—Gottlob Frege (1848–1925)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)
“‘Tis no extravagant arithmetic to say, that for every ten jokes,—thou hast got an hundred enemies; and till thou hast gone on, and raised a swarm of wasps about thine ears, and art half stung to death by them, thou wilt never be convinced it is so.”
—Laurence Sterne (1713–1768)