State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2)/(46.210)(1.01)106.798.2/46.2101.01 (b) (18.7)218.72 (c) (1.60×10−19)(3712)1.60×10−193712 .
Question
State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2)/(46.210)(1.01)106.798.2/46.2101.01 (b) (18.7)218.72 (c) (1.60×10−19)(3712)1.60×10−193712 .
Solution
(a) The rule for multiplication and division is that the result should have the same number of significant figures as the quantity with the least significant figures. In this case, 1.01 has the least number of significant figures (3). Therefore, the result should have 3 significant figures.
(b) The rule for exponentiation is that the number of significant figures in the result is the same as the number of significant figures in the original number. Therefore, the result should have 3 significant figures, the same as 18.7.
(c) The rule for multiplication is that the result should have the same number of significant figures as the quantity with the least significant figures. In this case, 1.60×10−19 has the least number of significant figures (3). Therefore, the result should have 3 significant figures.
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How many significant figures are present in the following?(i) 0.0025 (ii) 208 (iii) 5005 (iv) 126,000 (v) 500.0 (vi) 2.0034
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