Significant Figures Sig Figs What are Sig Figs

Significant Figures “Sig Figs”

What are Sig Figs? • the number of figures that are known with some degree of reliability • The number of digits used to express a measured or calculated quantity

Why Do We Use Sig Figs? • To show precise a number is

Determining if a Number is Significant • There are 5 rules to help determine the number of significant figures in a quantity

Rules for Significant Figures 1. Nonzero numbers are ALWAYS significant. = 4 Sig Figs 1287 g 78, 483 cm 58 m. L = 5 Sig Figs = 2 Sig Figs 638 mol = 3 Sig Figs

Rules for Significant Figures 2. Zeros in-between nonzero numbers are ALL significant. 101 mol = 3 Sig Figs 20, 375 cm = 5 Sig Figs 1001 J 908 s = 4 Sig Figs = 3 Sig Figs

Rules for Significant Figures 3. Zeros in front of nonzero digits (preceding zeros) are not significant. They are called place holders. 0. 78 Kg = 2 Sig Figs 0. 0309 cm = 3 Sig Figs 290 amp = 2 Sig Figs 300 s = 1 Sig Figs

Rules for Significant Figures 4. Zeros after nonzero numbers (trailing zeros) WITH A DECIMAL PRESENT are significant 6. 0 mg = 2 Sig Figs 678. 10 Kg = 5 Sig Figs 80. 0 m = 3 Sig Figs 12. 00 m. L = 4 Sig Figs

Rules for Significant Figures 5. Exact numbers and defined constants have an infinite number of significant figures. = Infinite Number of Sig Figs 1 dozen = 12 78 pencils 32 books 1 pair = 2 = Infinite Number of Sig Figs

Zeros that are significant. 202 cm = 3 Sig Figs 510002 L = 6 Sig Figs 144. 0 kg 670. 00 cd = 4 Sig Figs = 5 Sig Figs

Zeros that are NOT significant, PLACE HOLDERS. 50 g = 1 Sig Figs 0. 0072 m = 2 Sig Figs 0. 0321 J 9000 L = 3 Sig Figs = 1 Sig Figs

Zeros that are significant (called Trailing) and zeros that are not significant (call Place Holder). 80020 s = 4 Sig Figs 0. 00401 kg = 3 Sig Figs 0. 03020 Amp = 4 Sig Figs 10230 L = 4 Sig Figs

Making Calculations with Significant Digits • Multiplying and Dividing The final answer is rounded to have the same number of significant figures as the measurement with the least number of significant figures. 25000 cm 2 755 cm x 33 cm = 24915 92 m x 20 m = 1840 2000 m 2

0. 45 g 0. 894 g / 2. 0 g = 0. 447 g 40. 0 x 3. 8 = 152 1. 50 203 x 4589 = 931567 932000 10259 / 789 = 13. 00253485 96. 0 / 75. 0 = 1. 25 101 x 0. 020 = 2. 02 2. 0 13. 0

Making Calculations with Significant Digits Adding and Subtracting The final answer is rounded so that it has the same number of digits past the decimal as the measurement with the least number of digits past the decimal 120. 60 89. 001 + 6. 3 215. 901 215. 9

756. 05 − 23. 02 733. 03 + 9. 002 2. 32 45. 659 56. 981 733. 03 56. 98

− 45 32. 5 13