Significant figures are a fundamental concept in scientific measurements. They indicate which digits in a number are reliable and contribute to its accuracy, reflecting the limitations of the measuring instrument used. Understanding how to handle these figures correctly ensures that calculations do not imply a greater precision than the original measurements possess. This article details guidelines for determining significant figures during subtraction.
The Rule for Subtraction
When subtracting measurements, the rule for determining the number of significant figures in the result differs from multiplication or division. The precision of the answer is limited by the measurement that has the fewest decimal places. It is not about the total count of significant figures in the original numbers.
This principle ensures that the outcome of a subtraction does not appear more precise than the least precise measurement used in the calculation. For instance, if one measurement is known to the hundredths place and another only to the tenths place, the difference can only be reliably known to the tenths place. This approach maintains consistency with the inherent uncertainty of the initial data. The focus remains on the position of the last known decimal place rather than the overall number of reliable digits.
Applying the Rule with Examples
Consider a scenario where you subtract 2.34 meters from 15.6 meters. The number 15.6 has one decimal place, while 2.34 has two decimal places. Performing the initial subtraction yields 15.6 – 2.34 = 13.26. According to the rule, the result must be rounded to match the number with the fewest decimal places, which is 15.6 with one decimal place. Therefore, 13.26 is rounded to 13.3 meters.
Another example involves subtracting 0.057 grams from 12.8 grams. Here, 12.8 has one decimal place, and 0.057 has three decimal places. The raw subtraction provides 12.8 – 0.057 = 12.743. Since 12.8 is the least precise in terms of decimal places (one decimal place), the answer must be rounded to one decimal place. Consequently, 12.743 is rounded to 12.7 grams.
Imagine calculating the change in temperature from 37.55 degrees Celsius to 25.1 degrees Celsius. The measurement 37.55 has two decimal places, and 25.1 has one decimal place. Subtracting these values gives 37.55 – 25.1 = 12.45. Applying the rule, the result should be rounded to one decimal place because 25.1 has the fewest decimal places. Thus, the final answer is 12.5 degrees Celsius.
Important Considerations
The phrase “least precise” when applied to subtraction (and addition) specifically refers to the position of the last significant digit relative to the decimal point. This specific number dictates the precision of the final answer.
It is important to note that this same decimal-place rule also applies when performing addition. Both addition and subtraction operations are governed by the precision of the decimal places, unlike multiplication and division, which are governed by the total number of significant figures. Adhering to this rule ensures that calculated values accurately reflect the reliability and limitations of the original measurements.