1 2 Significant Figures Rules and Calculations Section

1 -2 Significant Figures: Rules and Calculations (Section 2. 5, p. 23 -28)

Rules for Sig Figs in Numbers: • • • Nonzero digits are ALWAYS significant: 97. 3 m has 3 sig figs “Leading” zeroes are NEVER significant: 0. 02 km has 1 sig fig These zeroes simply act as placeholders “Captive” zeroes are ALWAYS significant: 304 sec has 3 sig figs “Trailing” zeroes with a decimal (anywhere) are significant: 4. 100 m has 4 sig figs “Trailing” zeroes without a decimal are NOT significant: 700 m has 1 sig fig “Exact” or counting numbers have no sig figs: 3 pens has no sig figs

Practice for you • 100 m = ____ 1 sig figs vs. 100. m = ____ 3 sig figs 1 sig figs • 0. 003 L = ____ 5 sig figs • 0. 0010100 = ____ 4 sig figs 303. 0 cm = ____

Rules for Significant Figures in Calculations: • Addition and Subtraction: Add or subtract all numbers; the answer has as many decimal places as the least accurate number. Example: • 677 • 9. 2 • + 6. 33 • 722. 53 • but since the first number is only reported to the 1’s place, the answer with sig figs would be 723

Multiplication and Division • Multiply and divide all the numbers and report the answer with as many sig figs as the number with the fewest sig figs. Example: • 22. 1 x 9. 234 = 204. 7 but since 22. 1 has three sig figs, the answer should be reported as 204

Misc Sig Fig Rules: For scientific notation, look to the # before the x 10: 3. 01 x 102 has 3 sig figs Round 5’s up. Besides using a. to indicate significance, an underline can also be used: 300. m = 3 sig figs = 300 m • Numbers in conversions are “exact”, with no sig figs: 1 kg = 1000 g • The 1000 has no sig figs associated with it. • 10. cm = 0. 10 m = 0. 0010 km Note how all have 2 sig figs • •

To practice sig figs and get immediate feedback on accuracy, go to: • http: //science. widener. edu/svb/tutorial/index. html