Significant Figures and Conversions It would be difficult

Significant Figures and Conversions

�It would be difficult to measure the width of this 2× 4 to better than a millimeter.

Uncertainty �We do not know infinite digits of a measurement �Exact numbers are known for sure �Inexact – have some question (estimates)

Reporting Numbers �In recorded numbers, all the digits are considered exact up until the last digit which may be off by one 8. 8 ±. 1 �All digits including the uncertain one are called significant figures �We are fairly confident of these digits

Read to the correct number of significant figures

Which Digits Are Significant? �Any non-zero number is significant �Any number to the left of a decimal is significant �Zeros to the right of a decimal and behind other numbers are significant �Zeros to the right of a decimal but in front of other numbers are not significant

How many Significant Figures in each below? 1) 2) 3) 4) 5) 6) 7) 8) 28. 6 910 0. 0076000 0. 0144030 400 700. 0 0. 4004 1. 30 3440. 10) 0. 04604 11) 804. 05 12) 1002 13) 400. 14) 0. 000625000 15) 6000 16) 0. 00067 9)

Round each to 3 Significant Figures 1) 2) 3) 4) 5) 6) 31. 068 2. 613 81. 436 0. 001567 149. 51 143. 81

Multiplying and Dividing �Multiply or divide the number out as normal but round the answer to the least number of significant figures in the problem

Solve each with correct Sig Figs 1) 2) 3) 4) 5) 2. 4 x 15. 82 = 94. 20 3. 16722 = (5. 682 x 105) x (2. 87 x 104) = (2. 145 x 10 -5) (6. 75 x 104) = 2. 5 cm x 0. 00875 km =

Addition and Subtraction �Add or subtract as normal but round the answer with the same number of decimal places as the quantity in the calculation having the least

Solve each with correct Sig Figs 1) 2) 3) 4) 5) 5. 44 – 2. 6103 2. 099 + 0. 05681 87. 3 – 1. 655 6. 078 + 0. 3329 2. 3 cm + 7. 7μm + 1. 91 m =

Conversions �Often the units must be changed in order to do a problem �Conversion factor method is utilized �See conversion factor chart at end of the book

Examples 1) 2) 3) 4) 5) 6) 7) 8) How many cm in 118 in? If there are. 24 L in one cup, how many liters in 26 cups? How many L in 6. 5 gal? 40 L = ____gal 850 cm = _____in 4. 5 L = _____cups How many cm 2 are in 35. 5 square inches? How many cubic meters in 1575 ft 3?