1.11
계산의 유효 숫자
정확한 유효 숫자 수를 사용하여 계산 결과를 보고하면 측정의 불확실성을 피할 수 있습니다. 이는 숫자 반올림에 대한 다음 규칙에 따라 결정될 수 있습니다:
- 숫자를 더하거나 뺄 때 소수점 이하 자릿수가 가장 작은 숫자와 동일한 소수점 이하 자릿수로 결과를 반올림하세요.
- …
유효 숫자는 수학 연산에서도 확실성을 달성하는 데 도움이 됩니다. 더하기 또는 빼기, 결과는 소수점 이하 자릿수가 가장 적은 측정값과 동일한 소수점 이하 자릿수를 갖도록 반올림해야 합니다.
마지막 숫자가 5 미만일 때 반올림을 수행하고 5 이상일 때 반올림을 수행해야 합니다. 마지막 숫자가 5일 때 다른 반올림 방법이 사용되는 경우가 있습니다.
예를 들어 2.052와 1.2의 합은 3.3으로 반올림됩니다.
그러나 곱하거나 나누는 동안 결과는 가장 적은 유효 숫자를 가진 측정값과 동일한 수의 유효 숫자를 갖도록 반올림되어야 합니다. 따라서 2.052와 1.2의 곱은 2.5로 반올림됩니다.
View the full transcript and gain access to JoVE Core videos
Q1: How do significant figures apply to addition and subtraction calculations?
In addition or subtraction, round the result to the same number of decimal places as the measurement with the fewest decimal places. For example, adding 2.052 and 1.2 yields 3.252, which rounds to 3.3 because 1.2 has only one decimal place. This ensures your answer reflects the precision of your least precise measurement.
Q2: What rounding rule applies when the last digit is exactly 5?
When the digit to be dropped is 5 or greater, round up and increase the retained digit by one. However, alternative rounding methods exist when the dropped digit is exactly 5, such as rounding to the nearest even value. These methods help minimize rounding errors in multistep calculations.
Q3: How do significant figures differ between multiplication and division versus addition and subtraction?
In multiplication or division, round the result to have the same number of significant figures as the measurement with the fewest significant figures. For instance, multiplying 2.052 by 1.2 gives 2.4624, rounded to 2.5. This differs from addition and subtraction, which use decimal places instead.
Q4: When should rounding be performed in multistep calculations?
Rounding should preferably be done at the end of a multistep calculation rather than after each step. This practice avoids the accumulation of rounding errors at each intermediate stage, ensuring your final result maintains the correct precision and certainty of the measured values.
Q5: What does rounding down mean when working with significant figures?
Rounding down occurs when the digit to be dropped is less than 5. In this case, leave the retained digit unchanged. For example, if you need to round 3.24 to one decimal place, the digit 4 is less than 5, so you round down to 3.2.
Q6: Why is reporting results with correct significant figures important for measurement uncertainty?
Reporting results with the correct number of significant figures reduces measurement uncertainty and accurately represents the certainty of measured values. Proper rounding prevents false precision and communicates the reliability of your data, which is essential for scientific accuracy and reproducibility.
Q7: How do you determine which measurement has the fewest significant figures in a calculation?
Count all non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point in each measurement. The measurement with the lowest count has the fewest significant figures. Your final answer must match this count when multiplying or dividing, ensuring consistency across all values.