Rounding Off Numbers
In correcting a number to express the proper number of sig. fig., we often have to drop off unwanted digits. The rules for rounding off numbers are explained in your textbook and/or lab manual. Here is a summary:
Rules for rounding off numbers:
If the digit immediately to the right of the last sig. fig. is more than 5, you round up.
If the digit immediately to the right of the last sig. fig. is less than 5, you round down.
35.76 in 3 sig. fig. is 35.8 (round up because it is more than half-way between 35.7 and 35.8)
35.74 in 3 sig. fig. is 35.7 (round down because it is less than half-way between 35.7 and 35.8)
If the digit immediately to the right of the last sig. fig. is equal to 5, you round up if the last sig. fig. is odd. You round down if the last sig. fig. is even. You round up if 5 is followed by nonzero digits, regardless of whether the last sig. fig. is odd or even.
24.35 in 3 sig. fig. is 24.4 (round up because last sig. digit is 3, an odd number)
24.25 in 3 sig. fig. is 24.2 (round down because last sig. digit is 2, an even number)
24.258 in 3 sig. fig. is 24.3 (round up because the digits 58 means it is past halfway to 24.3)
After rounding off, if the resulting number has ambiguous zeroes, it should be recorded in scientific notation to avoid ambiguity.
34821.0 in 2 sig. fig. is 35000 where the three zeroes may or may not be significant.
The correct answer is 3.5 x 10 4 .
Try these problems:
72.49 in 3 sig. fig. is ___________ 299000 in 2 sig. fig. is ___________
45.52 in 3 sig. fig. is ___________ 92,528 in 4 sig. fig. is ___________
120.05 in 4 sig. fig. is ___________ 13,052 in 3 sig. fig. is ___________
239.5 in 3 sig. fig. is ___________ 2.448 x 104 in 3 sig. fig. is ___________
28.149 in 3 sig. fig. is ___________ 32000.000 in 3 sig. fig. is ___________
63500 in 2 sig. fig. is ___________ 89999 in 3 sig. fig. is ___________
Answers are shown below:
|
72.49 in 3 sig. fig. is 72.5 |
299000 in 2 sig. fig. is 3.0 x 105 |
|
45.52 in 3 sig. fig. is 45.5 |
92,528 in 4 sig. fig. is 9.253 x 104 |
|
120.05 in 4 sig. fig. is 120.0 |
13,052 in 3 sig. fig. is 1.31 x 104 |
|
239.5 in 3 sig. fig. is 2.40 x 102 |
2.448 x 104 in 3 sig. fig. is 2.448 x 104 |
|
28.149 in 3 sig. fig. is 28.1 |
32000.000 in 3 sig. fig. is 3.20 x 104 |
|
63500 in 2 sig. fig. is 6.4 x 104 |
89999 in 3 sig. fig. is _9.00 x 104 |