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:
“O! O! another stroke! that makes the third.
He stabs me to the heart against my wish.
If that be so, thy state of health is poor;
But thine arithmetic is quite correct.”
—A.E. (Alfred Edward)
“Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.”
—Ralph Waldo Emerson (1803–1882)
“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)