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Rounding and Significant Digits (page 2 of 3) Sections: General rounding, Rounding and significant digits Another consideration in rounding is when you have to round to "an appropriate number of significant digits". What are significant digits? Well, they're sort of the "interesting" or "important" digits. For example, 3.14159 has six significant digits (all the numbers give useful information) 1000 has one significant digit (only the 1 is interesting; you don't know anything for sure about the hundreds, tens, or units places; the zeroes may just be placeholders) 1000.0 has five significant digits (the ".0" tells us something interesting about the presumed accuracy of the measurement being made: that the measurement is accurate to the tenths place, but that there happen to be zero tenths) 0.00035 has two significant digits (only the 3 and 5 tell us something; the other zeroes are placeholders) 0.000350 has three significant digits (that last zero tells us that the measurement was made accurate to that last digit, which just happened to be zero) 1006 has four significant digits (the 1 and 6 are interesting, and we have to count the zeroes, because they're between the two interesting numbers) 560 has two significant digits (the last zero is just a placeholder) 560. (notice the "point" after the zero) has three significant digits (the decimal point tells us that the measurement was made to the nearest unit, so the zero is not just a placeholder) 560.0 has four significant digits (the zero in the tenths place means that the measurement was made accurate to the tenths place, and that there just happen to be zero tenths; the 5 and 6 give useful information, and the other zero is between significant digits, and must therefore also be counted) If you need to express your answer as being "accurate to" a certain place, here's how the language works with the above examples: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved 3.14159 is accurate to the hundred-thousandths place 1000 is accurate to the thousands place 1000.0 is accurate to the tenths place 0.00035 is accurate to the hundred-thousandths place 0.000350 is accurate to the millionths place (note the extra zero) 1006 is accurate to the units place 560 is accurate to the tens place 560. is accurate to the units place (note the decimal point) 560.0 is accurate to the tenths place Here are the basic rules: 1) All nonzero digits are significant. The real question comes in how to round answers to the "appropriate" number of significant digits. Often, they've given you a couple numbers and had you multiply them, and you're supposed to come up with a "reasonable" real-world answer. The idea is this: Suppose you measure a block of wood. The length is 5.6 inches, the width is 4.4 inches, and the thickness is 1.7 inches, at least as best you can tell from your tape measure. To find the volume, you would multiply these three dimensions, to get 41.888 cubic inches. But can you really, with a straight face, claim to have measured the volume of that block of wood to the nearest thousandth of a cubic inch?!? Not hardly! Each of your measurements was accurate (as far as you can tell) to two significant digits. Then you can only claim two significant digits in your answer. In other words, the "appropriate" number of significant digits is two, and you would report (in your physics lab report, for instance) that the volume of the block is 42 cubic inches. Here are some rounding examples; each number is rounded to four, three, and two significant digits.
742,400
(four significant digits)
0.07284
(four significant digits)
231.5
(four significant digits) << Previous Top | 1 | 2 | 3 | Return to Index Next >>
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Copyright © 2006-2008 Elizabeth Stapel | About | Terms of Use |
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