Significant Figures

Rules for Measurement When measuring, significant figures are the reliable digits. The last digit in a measurement usually shhow uncertainty, and makes all digits after the last number insignificant. There are four rules to significant figures. o 1. All digits listed with a value of 1-9 are considered significant. Ex: 25 has 2 sig figs, 5.67 has 3 sig figs. o 2. All 0s that are between non-zero digits (sandwiched) are significant. Ex: 308 has 3 sig figs, has 4 sig figs. o 3. All leading 0s are NEVER significant. Ex: 045 has 2 sig figs, has 3 sig figs. o 4. Ending 0s are only significant when a decimal is present in the value. Ex: 1,000 has 1 sig fig, 1,000.0 has 5 sig figs, 5.00 has 3 sig figs. Numbers in scientific notation ( 3.57 x 10 8 ) use the coefficient for sig figs. o Ex: 4.58 x 10 5 has 3 sig figs, x has 4 sig figs Extra examples: 12,045.0 has 6 sig figs; has 3 sig figs, has 5 sig figs.

Sig Figs with Math While using significant figures with multiplication/division, your answer can only have the same amount of sig figs as the number with the least in the equation. The first digit past the amount of sig figs you can have is used to round the value. o Ex: 45.0 m x m = m 2 ; since 45.0 only has 3 sig figs the answer can only have 3 sig figs as well. Your final answer would be 70.0 m 2. o Ex: g / mL = ; you can only have 4 sig figs due to so your final answer would be g/mL.

Sig Figs with Math When adding/subtracting with significant figures, your answer can only extend to the value with the largest placement of digits. In other words, if one value has sig figs in the tenths position, and another that is added to this value has sig figs to the hundredths position, the tenths is a larger placement so the answer can only extend to the tenths position. o Ex: 1.56 cm cm = 4.06 cm; since 2.5 only places sig figs to the tenths position, your answer can only go to the same position and would be 4.1 cm. o Ex: m – m = m; since only places sig figs to the hundredths position, your answer can only place sig figs to the same position and would be m.

Sig Figs with Math When using both multiplication/division and addition/subtraction in the same equation with measured values, you switch rules when going from one type of math (m/d or a/s) to the other. Follow PEMDAS to work through the equation properly. o Ex: (5.6 g – 1.34 g) / 1.34 mL = g/mL; you would use the addition/subtraction rule and get 4.3 g inside the parenthesis, then use the multiplication/division rule to divide 4.3 g by 1.34 mL to get 3.2 g/mL as your final answer. When counting, significant figures are infinite and should not be considered. Only significant figures from measurements should be considered. o Ex: Timmy counted 47 apples on an apple tree that he measured to be 5.5 m in height. The apples counted should not be considered for sig figs, but the height of the tree should be used with proper sig figs.