Measurement and Significant figures


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Significant figures are those digits in a measured number or result of a caluation with measured numbers that include all certain digits  plus a final one having some uncertainity.

For example; When you measure a rod and you obtain the values 9.12 cm, 9.11 cm and 9.13 cm.You could reposrt the results as the average 9.12 cm .In this case first two digit 9.1 are certain;the next digit is estimated so it has some degree of certainity.

Number of significant  figures : This refers to the number of digits reported for the value of a measured or calculated quantity, indicating the precision of the value.Thus, there are three significant figures in 9.12 cm.To count the number of significant figure we need to follow some rules, that are illiustrated below;

Rule 1 ; All digits are significant except zeros at the begning of the number & possibly terminal zeros (one or more at the end of a number).Thus, 9.12 cm,0.912,0.00912 cm all contain three significant figures)

Rule 2: Terminal zeros ending at the right of the decimal point are significant.Like each of these numbers have three significant figures;9.00cm,9.10cm,90.0cm

Rule 3; Terminal zeros in a number without an explicit decimal point may or may not be significant.If you are given measurement as 900 cm, you do not know whether one, two or three significant figures are intended.If you are given 900. cm the zeros are significant.

Significant figure in Calculations

 Rule for multiplication and division ;When multiplying or dividing measured quantities, give as many significant figures in the answer as there are in the measurement with least number of significant figures. For exampl; 6.038 x 2.57 = 15.5177 ( the number with least sig fig is 2.57 3 sig fig)
= 15.5 ( correct answer with 3 sig fig.)
Rule for addition and substraction ; In addition and subtraction of a series of measuremnts, the number of significant figure decided by the fact that answer must have same number of digits to the right of the decimal as the original value having fewest number of digitss to the right of decimal.When adding or subtracting arrange the value so that the decimal points align.Identify value with fewest places after decimal point and round answer to that number of places.

Rounding off number:-Deleting non significant digits from a calculated number.
Rule 1- If first digit to be dropped is less than 5, that digits and all digit followed it are simply dropped.For ex; 62.312 rounded off to 3 sig fig becomes 62.3.
Rule2- If first digit to be dropped is greater than or equal to 5 followed by digits other than zeros, the excess digits are all dropped and last retained digits in increased in value by one unit.For ex; 62.782 and 62.558 rounded to 3 sig. fig becomes 62.8 and 62.6 respectively.
Rule 3 - If first digit to be dropped is equal to 5 not followed by any other digits or followed only by zeros, an odd-even rule applies.Drop 5 and any zero that follow it and then
A)Increase last retained digit by one unit if it is odd.For ex-62.350 rounded to 3 sig fig become 62.4
B)Leave last digit unchanged if it is even.For example- 62.650 rounded to 3 sig. fig becomes 62.6