Rounding off Significant numbers | Significant figures rounding

To get a better precision in measurement, we need to round off the numbers up to some significant figures. Suppose we have to present a long decimal number 65.3452343….. up to two or three significant figures after the decimal. This may look straightforward, but it is not the case. The last digit may be the cause of an error in the presentation. There are some rules to present the data up to some digit after the decimal. This rule is known as rounding off a number. In this article, you are going to know the rules for rounding off significant numbers.

Rules for Rounding off significant numbers

Here are some rules for rounding off significant figures. Let, we need to round off a number up to three significant figures.

  1. If the fourth significant digit is less than 5, then the third significant digit will remain the same. The rounding-off value of 2.03234 up to three significant digit is 2.03. Because the fourth significant digits is 2 which is less than 5. So the third significant digit will remain the same (here it is 3).
  2. If the fourth significant digit is greater than 5 then we need to add 1 with the third significant digit. In 2.03634, the rounding off value is 2.04 as the fourth significant digit is 6.
  3. If the fourth significant digit is 5 and there is a non-zero digit after 5, then again we need to add 1 with the third significant digit. In 2.035134 the rounding off value up to three significant digits is 2.04.
  4. If the fourth significant digit is 5 and there is 0 or there is no digit after this 5 then i) if the third significant digit is odd then we need to add 1 with the third significant digit and ii) if the third significant digit is even then it will remain as it is. For example: in the number 2.035 or 2.0350 the rounding off value is 2.04. Again, in 2.025 or 2.0250 the rounding off value is 2.02.

Homework Problems: Find the rounding of values up to two significant digits for the numbers i) 2.04 ii) 2.27 iii) 0.589

Note: If it is asked to round the number up to three significant figures after the decimal, then the number before the decimal will be as it is, but after the decimal, we need to round the numbers up to three significant digits.

For example, The rounding off value of 2.03234 up to three significant figures after the decimal is 2.032. (See the difference between the example in rule-1 and this example).

Problems on Significant figures rounding

Question: Round the numbers up to four significant figures – i) 37.25894 ii) 2.034589 iii) 0.0028645

Answers:

i) Here, the fourth digit is 5 and the next digit is present. So, the rounding-off value of 37.25894 up to four significant digits is 37.26.

ii) The rounding off value of 2.034589 up to four significant digits is 2.035. Here, one should be added to the fourth digit 4.

iii) The zeros at the beginning are not significant. Then the fourth significant digit is 4. The very next digit is 5 and there are no other digits after 5. Since the fourth significant digit (4) is even then it will remain as it is. Thus, the rounded off value of 0.0028645 up to four significant digits is 0.0022864.

In this way, one can round a number up to some significant figures. This is all from this article on Rounding off. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

Related posts:

  1. Rules for Significant figures in Calculations

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