Introduction to significant figures rounding rules:
The significant figures are normally those digits in a measured quantity which is known reliably or the ones we are confident of in our measurement plus one additional digit that is uncertain. The number of significant figures in a measurement is directly proportional to the measurement's accuracy. Suppose the time period of the simple pendulum is 1.62 seconds. This digit 1 and 6 are reliable and certain, while the digit 2 is uncertain. So, the time period has significant figures that are three in total. Again, the length of the object measured as 273.6 cm. It has four significant figures. The digits 2, 7 and 3 are certain while the digit 6 is uncertain. Here we discuss the rules for the rounding of the significant figures in any particular measurement.
Significant Figures Rounding Rules:
The significant figures rounding rules are as follows:
(i) If the digit which would be dropped is lesser than 5, in that case, the preceding digit will be unchanged.
(ii) If the digit which would be dropped is bigger than 5, which would be the preceding digit will be increased by 1.
(iii) If the digit which would be dropped is 5 followed by the non zero digits, in that case, the preceding digit will be increased by 1.
(iv) If the digit which would be dropped is 5, in that case, the preceding digit is left unchanged if it is even.
(v) If the digit which would be dropped is 5, in that case, the preceding digit is increased by 1 if it is odd.
Understanding how to find the least common multiple is always challenging for me but thanks to all math help websites to help me out.
Examples for the Significant Figures Rounding Rules:
Round off the following numbers as indicated:
(a) 18.35 upto 3 digits
(b) 143.45 upto 4 digits
(c) 18967 upto 3 digits
Solution
(a) Here the third digit is 3 (odd number) and the next digit is 5 so that the digit 3 is increased by 1. Hence, the rounded figure is 18.4
(b) Here the fourth digit is 4 (even number) and the next digit is 5 so that the digit 4 is remained same. Hence, the rounded figure is 143.4.
(c) Here the third digit is 9 and the next digit is 6 which is more than 5 so that the preceding digit is increased by 1. Hence, the rounded figure is 19000.
The significant figures are normally those digits in a measured quantity which is known reliably or the ones we are confident of in our measurement plus one additional digit that is uncertain. The number of significant figures in a measurement is directly proportional to the measurement's accuracy. Suppose the time period of the simple pendulum is 1.62 seconds. This digit 1 and 6 are reliable and certain, while the digit 2 is uncertain. So, the time period has significant figures that are three in total. Again, the length of the object measured as 273.6 cm. It has four significant figures. The digits 2, 7 and 3 are certain while the digit 6 is uncertain. Here we discuss the rules for the rounding of the significant figures in any particular measurement.
Significant Figures Rounding Rules:
The significant figures rounding rules are as follows:
(i) If the digit which would be dropped is lesser than 5, in that case, the preceding digit will be unchanged.
(ii) If the digit which would be dropped is bigger than 5, which would be the preceding digit will be increased by 1.
(iii) If the digit which would be dropped is 5 followed by the non zero digits, in that case, the preceding digit will be increased by 1.
(iv) If the digit which would be dropped is 5, in that case, the preceding digit is left unchanged if it is even.
(v) If the digit which would be dropped is 5, in that case, the preceding digit is increased by 1 if it is odd.
Understanding how to find the least common multiple is always challenging for me but thanks to all math help websites to help me out.
Examples for the Significant Figures Rounding Rules:
Round off the following numbers as indicated:
(a) 18.35 upto 3 digits
(b) 143.45 upto 4 digits
(c) 18967 upto 3 digits
Solution
(a) Here the third digit is 3 (odd number) and the next digit is 5 so that the digit 3 is increased by 1. Hence, the rounded figure is 18.4
(b) Here the fourth digit is 4 (even number) and the next digit is 5 so that the digit 4 is remained same. Hence, the rounded figure is 143.4.
(c) Here the third digit is 9 and the next digit is 6 which is more than 5 so that the preceding digit is increased by 1. Hence, the rounded figure is 19000.
