Addition and Subtraction Using Significance Arithmetic
When adding or subtracting using significant figures rules, results are rounded to the position of the least significant digit in the most uncertain of the numbers being summed (or subtracted). That is, the result is rounded to the last digit that is significant in each of the numbers being summed. Here the position of the significant figures is important, but the quantity of significant figures is irrelevant. Some examples using these rules:
- 1 + 1.1 = 2
- 1 is significant to the ones place, 1.1 is significant to the tenths place. Of the two, the least accurate is the ones place. The answer cannot have any significant figures past the ones place.
- 1.0 + 1.1 = 2.1
- 1.0 and 1.1 are significant to the tenths place, so the answer will also have a number in the tenths place.
- 100 + 110 = 200
- 100 is significant to the hundreds place, while 110 is significant to the tens place. Therefore, the answer must be rounded to the nearest hundred.
- 100. + 110. = 210.
- 100. and 110. are both significant to the ones place (as indicated by the decimal), so the answer is also significant to the ones place.
- 1×102 + 1.1×102 = 2×102
- 100 is significant up to the hundreds place, while 110 is up to the tens place. Of the two, the least accurate is the hundreds place. The answer should not have significant digits past the hundreds place.
- 1.0×102 + 111 = 2.1×102
- 1.0×102 is significant up to the tens place while 111 has numbers up until the ones place. The answer will have no significant figures past the tens place.
- 123.25 + 46.0 + 86.26 = 255.5
- 123.25 and 86.26 are significant until the hundredths place while 46.0 is only significant until the tenths place. The answer will be significant up until the tenths place.
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