Exact and Inexact Numbers

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Presentation transcript:

Exact and Inexact Numbers Significant Figures Exact and Inexact Numbers

Significant Figures All measured numbers are inexact Exact numbers are often found as conversion factors or as counts of objects. They can also be by definition such as a dozen or 3 feet in a yard. Exact numbers can be considered to have an infinite number of significant figures. Therefore the number of apparent significant figures in any exact number can be ignored as a limiting factor in determining the number of significant figures in the result of a calculation.

Significant Figures Rules for deciding the number of significant figures in a measured quantity: 1) All nonzero digits are significant: 3.254 g has 4 significant figures. 3.3 g has 2 significant figures. 2) Zeroes between nonzero digits are significant: 107 kg has 3 significant figures 1007 kg has 4 significant figures

Significant Figures 3) Zeroes to the left of the first nonzero digits are not significant. These zeroes only indicate the position of the decimal point: 0.004 G has 1 significant figure. 0.042 g has 2 significant figures. 4) Zeroes to the right of a decimal point in a number are significant: 4.20 mL Has 3 significant Figures 4.200 ml has 4 significant figures 4200. Ml has 4 significant figures

Significant Figures 4.3400 x 104 5 sig figs 4.340 x 104 4 sig figs

Multiplying & Dividing with significant Figures The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer. Multiply or divide Then Round to get the correct answer