SIGNIFICANT FIGURES (Sig Figs)

1. SIGNIFICANT • FIGURES • (Sig Figs)

2. 3.1 • Suppose you estimate a length that is between 2.4 cm and 2.5 cm to be 2.45 cm. • The first two digits (2 and 4) are known. The last digit (5) is an estimate and involves some uncertainty. • All three digits convey useful information, however, and are called significant figures. • Significant Figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

3. REMEMBER!!!!!!!!!!!! • When recording a reading from a piece of equipment with markings (ex. ruler, graduated cylinder) • always record to one place beyond the lowest value marking; the last digit recorded is the estimated digit

4. 3.1 Significant Figures in Measurements • Significant Figures in Measurements • Measurements must always be reported to the correct number of significant figures because accuracy of answers calculated using those measurements depend on the number of sig figs in the values for in the calculation.

5. we must follow rules when calculating with measurements so that the final answer is not more accurate than any of the original measurements • therefore, you need to know how many SF are in a number before you can carry out calculations properly

6. RULES TO DETERMINE HOW MANY SIG FIGS IN A NUMBER • ALL DIGITS 1 TO 9 ARE SIGNIFICANT • ex: 914, .0235, 408, and 67300 all have 3 SF • sometimes zeros are significant • ZEROS BETWEEN NON-ZERO DIGITS (EMBEDDED) ARE ALWAYSSIGNIFICANT • ex: 7003 m, 40.79 m, and 1.503 m all have 4 SF

7. 3. ZEROS AT THE BEGINNING OF A NUMBER (LEADING ZEROS) ARE NEVER SIGNIFICANT • ex: 0.00305, .0267, 0.123 all have 3 SF • 4. ZEROS AT THE END OF A NUMBER (TRAILING ZEROS) ARE ONLY SIGNIFICANT WHEN THERE IS A DECIMAL ANYWHERE IN THE NUMBER • A. a decimal anywhere in the number, trailing zeros are significant • ex: 0.12300, 1960.0 , 28.370 all have 5 SF • B. a decimal not present in the number, trailing zeros are NOT significant • ex: 19650, 3 505 000, 20020 all have 4 SF

8. 5. a bar on top of a number indicates the last significant digit • 6. there are two situations with unlimited number of sig figs • counting ex: 23 people • exactly defined quantities • w/in a system of measurement ex: 1L=1000mL 1 SF 2 SF 3 SF 4 SF

9. 3 SF • 5 • 5 • unlimited • 4 • 2

10. PRACTICE SIG FIGS AND WRITING SN • 0.0045088 = 5 SF • 4.5088 x 10-3 = 5 SF • 2850. = • = 4 SF • 2850 = 3 SF • = 3 SF A given value must have the same number of SF no matter how it is written! 4 SF 2.850 x 103 2.85 x 103

11. SIG FIG VIDEO

12. 3.1 Section Quiz • 1. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement? • 2 • 3 • 4 • 5

13. 3.1 Significant Figures in Measurements

14. I don’t use the rest anymore 9/10

15. Atlantic Pacific • FOR ZEROS AT THE BEGINNING OF A NUMBER (.0035) OR AT THE END OF A NUMBER (3500) FOLLOW THIS EASY PROCEDURE: • think about a map of the USA with the Pacific Ocean on the left and the Atlantic Ocean on the right

16. if a decimal point is present, count from the pacific side, starting with the first non-zero number and continue counting until the end • 0.0045088 = 5 SF • 4.5088 x 10-3 = 5 SF • 2850. = • = 4 SF • if a decimal point is absent, count from the atlantic side, starting with the first non-zero number and continue counting until the end • 2850 = 3 SF • = 3 SF A given value must have the same number of SF no matter how it is written! 4 SF 2.850 x 103 2.85 x 103