Measurement

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Physics Newtonian Mechanics Measurement

	Precision and Significant Figures:
	When physical quantities are measured, the measured values are known only to within the limits of the experimental uncertainty. The value of this uncertainty can depend on various factors, such as the quality of the apparatus, the skill of the experimenter, and the number of measurements performed. For example, the area of a computer disk level is to be measured. The accuracy matters here. Suppose the length is measured as 6.4 cm though its values lie in between 6.3 cm and 6.5 cm with an accuracy of the stick to be ± 0.1 cm. Thus, the length is (6.4±0.1) cm. Similarly its width is measured as (5.5 ± 0.1) cm. Now the area would be the product of 6.4 cm and 5.5 cm which is 35.2 cm². However, it is not justifiable to write this value since both length and width have two digits where as the result has three. Here comes the importance of the digits that we finally write. These digits are called significant figures. There are certain rules for dealing with the significant figures: 1. When multiplying several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the least accurate of the quantities being multiplied, where “least accurate” means “having the lowest number of significant figures”. The same rule applies to division as well. 2. Zeros may or may not be significant figures. Those used to position the decimal point in such numbers 0.03 and 0.0075 are not significant. Thus, there are one and two significant figures respectively, in these two values. When the zeros come after other digits are significant. 3. When numbers are added or subtracted, the number of decimal places in the result should be equal to the smallest number of decimal places of any term in the sum. 4. It is always better to use the scientific notation to indicate the number of significant figures. For example if the mass of a substance is 1500 kg then the mass would be expressed as 1.50 × 103 kg provided there are three significant figures in the measured value.