1. SIGNIFICANT FIGURES Fun With Numbers!!

2. 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!

3. Rules for deciding the number of significant figures in a measured quantity: (1)All NON_ZERO DIGITS are significant: 1.234 g has 4 significant figures, 1.2 g has 2 significant figures.

4. 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.

5. 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: 0.001 o C has 1 significant figure, 0.012 g has 2 significant figures.

6. 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: 0.023 mL has 2 significant figures, 0.200 g has 3 significant figures.

7. 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

8. 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) 5.060 × 10 4 calories (4 significant figures), or 5.0600 × 10 4 calories (5 significant figures).

9. 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 12000000. Or 10.

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.

11. 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.

12. 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). 100. + 23.643 = 123.643, which should be rounded to 124

13. CALCULATING WITH SIGNIFICANT FIGURES: (2) In multiplication and division, the result should be rounded off TO THE LEAST NUMBER OF SIGNIFICANT FIGURES 3.0 × 12.60 = 37.800 which should be rounded off to 38

14. EXAMPLES: 1.4.75 + 2.3 2.1.75 * 2 3.0.0075 / 1.007 4.1200 * 4.25 5.17.50 – 9.375 = 7.05 ~ 7.1 = 3.50 ~ 4 = 0.007447869… ~0.0074 = 5100 ~ 5100 or 5.1 x 10 3 = 8.125 ~8.13