Chemistry · Ch 2 — Introduction to Analytical Chemistry
Calculations with significant figures
Calculations with significant figures
When several measured quantities are combined in a calculation, the accuracy of the final result is limited by the accuracy of the least accurate (fewest-significant-figure) measurement used in that calculation — in other words, a calculation can never manufacture more precision than its least precise input possessed. Because of this, the raw result of a calculation very often contains more digits than are actually significant, and it must be rounded off to the appropriate number of significant figures before it is reported. Two simple rules govern this rounding. If the digit immediately following the last digit you intend to keep is LESS than five, the digit you are keeping is left unchanged and everything after it is simply dropped; for example, 46.32 rounded off to two significant figures becomes 46. If the digit immediately following the last digit you intend to keep is FIVE or more, the digit you are keeping is increased by one before everything after it is dropped; for example, 52.87 rounded off to three significant figures becomes 52.9. These same two rules are appli …
Worked out. Worked example applying the rounding-off rule to four numbers: (a) 1.223 rounded to two significant figures is 1.2, because the third digit (2) is less than 5, so it and everything after it is simply dropped. (b) 12.56 rounded to three significant figures is 12.6, because the fourth digit (6) is greater than 5, so it is dropped and the third digit is increased by one (5 becomes 6). (c) 122.17 rounded to four significant figures is 122.2, because the fifth digit (7) is greater than 5, so it is dropped and the fourth digit is increased by one (1 becomes 2). (d) 231.5 rounded to three significant figures is 232, because the fourth digit is exactly 5, so it is dropped and the th …