Subsection 1.1.1 Rounding off the Numbers
When rounding , we examine the digit following to the right of the digit that is to be the last digit in the rounded off number. The digit we are examining is the first digit to be dropped. If digit to be dropped off is less than 5, then drop it off with all the other digits to the right of it. If the digit to be dropped off is greater than 5, then increase the number by 1 to the preceeding digit to be rounded. If the digit to be dropped is 5, then round the preceeding digit so that it will become even number. Zero is considered to be even when rounding off. This is the process of minimizing systematic error.
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Round 742,396 to four, three, and two significant digits:
- To round to four sig. fig. start with the first significant digit, which is the 7. Then count to the right from there. The first four significant digits of 742,396 are the 7, the 4, the 2, and the 3. Just to the right of the 3 is a 9. Because this value is ”greater than 5”, round the 3 up to 4. Replace the remaining digits (the 9 and the 6) with zeroes. Then: 742,400 (four significant digits).
- To round 742,396 to three places, start again with the 7 and include the next two digits, being the 4 and the 2. Since the next digit is a 3, which is ”less than 5”, leave the 2 alone and don’t round up. Replace the three digits after the comma with zeroes. Then: 742,000 (three significant digits)
- To round 742,396 to two places, use only the first two digits, which are followed by a 2, so don’t round up. Instead, just replace the final four digits with zeroes, to get: 740,000 (two significant digits).
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Round 0.07284 to four, three, and two significant digits:
- To round 0.07284 to four significant digits, start with the first significant digit, which is the 7. (The zero between the decimal point and the 7 is not significant, as it serves only to ”place” the 7 into the hundreds place.) There are only three more digits, so all of them will be included in answer. Since no digit follows the 4, there is no information about rounding, so just leave the 4 as it is. Hence, 0.07284 is four sig-digs.
- When rounding 0.07284 to three sig-digs, the final sig-dig is the 8, which is followed by the 4. Since 4 is less than 5, so simply drop it. Because these sig-digs are after the decimal point, not replace the 4 with a zero. Hence, 0.0728 is three sig-digs.
- To round 0.07284 to two sig-digs, use the 7 and the 2. Since the 2 is followed by an 8, round the 2 up to 3; drop everything that follows. Hence, 0.073 is two sig-digs.
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Round 425.35 to four and two significant digits:
- For four sig.fig. this number is 425.4, because the value to be rounded off (3) is ”odd” and followed by a ”5”, then round the 3 up to 4 and remove the remaining digits.
- For two sig.fig. it would be 420, because the value to be rounded off (2) is ”even” and followed by a ”5”, then leave 2 as it is and replace the other with zeroes.
