Significant Figures

Accuracy and Precision Review What’s the difference in accuracy and precision? Are they the same thing? Are they related? Accuracy: Proximity to the true value Precision: Repeatability of the measurement

Precise and/or Accurate? High Precision Low Accuracy Low Precision High Accuracy High Precision High Accuracy

Rounding When rounding, look only at the first number on the right of your objective Example - Round 3.141592654 to the nearest: A.) 4 Decimal Places B.) 3 Decimal Places C.) 1 Decimal Place

Counting Sig Figs Why are Sig Figs Important? You can’t be more or less precise than what you are measuring with Nonzero Integer – Always significant! Example: 15 28,853 5.364

“Sandwiched” or “Wedgie”Zeros Any number(s) between two significant figures is significant, ALWAYS: 500000.0008 Ten Sig Figs 1.1074 Five Sig Figs

Leading Zeros Leading Zeros – Zeros that precede all the nonzero digits are NOT significant Ex. 0.000085 Two Sig Figs 0.000256 Three Sig Figs

Trailing Zeros Zeros that fall at the right end of a number Significant if after a decimal: 1.2500 Five Sig Figs Not Significant if before a decimal: 150,000 Two Sig Figs Examples 50.0 Three 50 One

An odd trailing zero… How many significant digits: 240 240.0 240. Two Four 240. Three The decimal on the end makes the last digit significant Practice: 50000. 5 Sig Figs only because of the decimal place

Exact Numbers Some numbers are exact Numbers from counting (3 Apples) Conversion Factors (1in = 2.54 cm) Exact numbers have an infinite number of significant figures

A Special Note Why do scientist like scientific notation? Significant digits can be vague without it All digits before the multiplier are significant, always! Example: 200 mL 2.0 X 102g

Pacific-Atlantic Rule

Practice – Think/Pair/Share Determine the number of significant figures in the following examples: 0.000304g 1.270 X 102 m 125g 10g 0.09020L 4.0 X 10-1 cm3

Rounding With Sig Figs How many sig figs are needed? You will be told! From the leftmost sig fig, count digits until you get to how many you need. Then round there. Example Round 1355 to three sig figs 1360 Round 0.0002564 to two sig figs 0.00026

Calculations with Sig Figs Multiplication and Division: Answer can have only as many significant figures as the measurement with the least significant digits Ex: 150.0/10 Addition and Subtraction The limiting term is the one with the smallest number of decimal places Ex: 5.5 + 11

Practice Determine the answer of the following. Be sure to include the correct significant digits A.) 17.1 + 0.77 + 241 = B.) 47.2 – 9 C.) 1.27 x 3.1416 D.) 0.072/4.36