1. In order to convey the appropriate uncertainty in a reported number, we must report it to the correct number of significant figures. 1-8 Significant Figures Significant figures Example The number 83.4 has three digits. All three digits are significant. The 8 and the 3 are "certain digits" while the 4 is the "uncertain digit."

2. The number 83.4 Thus, measured quantities are generally reported in such a way that only the last digit is uncertain. All digits, including the uncertain one, are called significant figures. This number implies uncertainty of plus or minus 0.1, or error of 1 part in 834.

3. Guidelines 457 cm (3 significant figures); 2.5 g (2 significant figures). 2. Zeros between nonzero digits are always significant 1005 kg (4 significant figures); 1.03 cm (3 significant figures). 0.02 g (one significant figure); 0.0026 cm (2 significant figures). 1. Nonzero digits are always significant 3. Zeros at the beginning of a number are never significant

4. 0.0200 g (3 significant figures); 3.0 cm (2 significant figures). 5. When a number ends in zeros but contains no decimal point, the zeros may or may not be significant 130 cm (2 or 3 significant figures); 10,300 g (3, 4, or 5 significant figures). 4. Zeros that fall at the end of a number or after the decimal point are always significant

5. To avoid ambiguity with regard to the number of significant figures in a number with tailing zeros but no decimal point, we use scientific (or exponential) notation to express the number. Example Scientific (or exponential) notation If we are reporting the number 700 to three significant figures, We can express it as 700 or 7.00 × 10 2

6. if there really should be only two significant figures we can write 7 × 10 2. if there should be only one significant figure, we can express this number as 7.0 × 10 2 Scientific notation is convenient for expressing the appropriate number of significant figures. It is also useful to report extremely large and extremely small numbers. the number 1.91 × 10 -24 we can express the number 0.00000000000000000000000191.

7. When measured numbers are used in a calculation, the precision of the result is limited by the precision of the measurements used to obtain that result. Significant figures in calculation If we measure the length of one side of a cube to be 1.35 cm, calculate the volume of the cube to be 2.460375 cm 3. Original number had three significant figures If we report the volume to seven significant figures, we are implying an uncertainty of 1 part in over two million! We can't do that.

8. Guidelines In order to report results of calculations so as to imply a realistic degree of uncertainty, we must follow the following rules. If A x B or A / B = C 1. The C must have the same number of significant figures as the A or B with the fewest significant figures. If A + B or A - B = C 2. The C can have only as many places to the right of the decimal point as the A or B with the smallest number of places to the right of the decimal point.

9. If we measure the length of one side of a cube to be 1.35 cm, The volume of the cube should to be 2.46 cm 3. Original number had three significant figures The significant figures of volume should not be more than three. Using above rules,

10. Question 1. What is the answer to the following problem, reported to the correct number of significant figures. The mass of 10 workbooks is 1.18 g. What is the mass of 1 workbook? 0.11807 g 0.1181 g 0.118 g 0.12 g 0.1 g

11. 2. How many significant figures are there in the number 0.0012? 1 2 3 4 5 3. How many significant figures are there in the number 1020.5? 2 3 4 5 6