SIGNIFICANT FIGURES Fun With Numbers!!. SIGNIFICANT FIGURES Significant figures are all numbers in a measurement that show the level of accuracy to which.

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Presentation transcript:

SIGNIFICANT FIGURES Fun With Numbers!!

SIGNIFICANT FIGURES Significant figures are all numbers in a measurement that show the level of accuracy to which a measurement has been made. They do more than just show the magnitude of the measurement!

Rules for deciding the number of significant figures in a measured quantity: (1)All NON_ZERO DIGITS are significant: g has 4 significant figures, 1.2 g has 2 significant figures.

Rules for deciding the number of significant figures in a measured quantity: (2) Zeroes BETWEEN nonzero digits are significant: 1002 kg has 4 significant figures, 3.07 mL has 3 significant figures.

Rules for deciding the number of significant figures in a measured quantity: (3) Zeroes to the left of the first nonzero digits are not significant; such zeroes merely indicate the magnitude or place value of the number: o C has 1 significant figure, g has 2 significant figures.

Rules for deciding the number of significant figures in a measured quantity: (4) Zeroes to the RIGHT of a decimal point AND a number are significant: mL has 2 significant figures, g has 3 significant figures.

Rules for deciding the number of significant figures in a measured quantity: (5) When a number ends in zeroes that are not to the right of a decimal point, the zeroes are NOT ALWAYS significant: 190 miles may be 3 or 2 significant figures, 50,600 calories may be 5, 4 or 3 significant figures

Rules for deciding the number of significant figures in a measured quantity: The potential ambiguity in the last rule can be avoided by the use of standard exponential, or SCIENTIFIC NOTATION. For example, depending on whether 3, 4, or 5 significant figures is correct, we could write 50,600 calories as: 5.06 × 10 4 calories (3 significant figures) × 10 4 calories (4 significant figures), or × 10 4 calories (5 significant figures).

Rules for deciding the number of significant figures in a measured quantity: Or by placing a decimal point after the last zero if all digits are significant, such as: 50,600. Or 100. Or Or 10.

Some numbers are exact because they are known with complete certainty. Most exact numbers are integers: exactly 12 inches are in a foot, there might be exactly 23 students in a class. Exact numbers are often found as CONVERSION FACTORS or as DEFINITIONS of objects. Exact numbers can be considered to have an INFINITELY number of significant figures.

CALCULATING WITH SIGNIFICANT FIGURES: In carrying out calculations, the general rule is that the accuracy of a calculated result is limited by the ACCURACY OF THE MEASUREMENTS involved in the calculation.

CALCULATING WITH SIGNIFICANT FIGURES: (1) In addition and subtraction, the result is rounded off to the COLUMN OF LEAST CERTAINTY (LEAST NUMBER OF DECIMAL PLACES) = , which should be rounded to 124

CALCULATING WITH SIGNIFICANT FIGURES: (2) In multiplication and division, the result should be rounded off TO THE LEAST NUMBER OF SIGNIFICANT FIGURES 3.0 × = which should be rounded off to 38

EXAMPLES: * / * – = 7.05 ~ 7.1 = 3.50 ~ 4 = … ~ = 5100 ~ 5100 or 5.1 x 10 3 = ~8.13