Measurements: Significant Figures

Transcription

1 Measurements: Significant Figures Significant figures: all digits in a number representing data or results that are known with certainty plus one uncertain digit. Ruler A: The last digit in a number associated with a measuring device is uncertain! Ruler B: Why you should care Let s say you plan to remodel your kitchen and you want to order new cabinets. Which ruler would you prefer? Please note that pictures are not to scale! 1

2 Measurements: Relevance of Significant Figures to Health Care Profession Scale A lbs Why you should care as a health professional? The answers are LIMITLESS! Below is one example. Anesthesia Dosage type of anesthetic patient s age patient s weight type of medication patient takes type of surgery Scale B 143 lbs When measuring your patient s weight, which scale you would prefer? Accuracy vs. Precision Accuracy: the degree of agreement between the true value and the measured value. Precision: a measure of the agreement of replicate measurements. Inaccurate & imprecise Inaccurate but precise Accurate & precise When taking a measurement, remember every measurement has some degree of error and uncertainty. the # of sig figs associated with the measuring device indicate how close repeat measurements will be to each other. 2

3 Rules for Determining Significant Figures All non-zero digits are significant. The number 436 has three sig figs. Zeroes located between non-zero digits are significant. The number has six sig figs. Leading zeroes (zeroes preceding the first non-zero integer) are insignificant. The number has four sig figs. Trailing zeroes (zeroes after the last non-zero integer) are significant if the number contains a decimal point. The number 70. has two sig figs. not significant if the number does not contain a decimal point. The number 2000 has one sig fig. How many significant figures are contained in each of the following numbers? 1, ,213, Just in Case You Forgot Your Places You don t have to memorize this! Look at the number closely and see if you can recognize a pattern! 3

4 Scientific Notation Mantissa between 1 and 10 + or Whole Number A 10 x Hint: To convert scientific notation into standard notation, move decimal x places to the right if positive or to the left if negative! A is easily generated by moving decimal point x places to the left until b/w 1 & 10. x is a positive and equal to the # of places the decimal point moved. A is easily generated by moving decimal point x places to the right until b/w 1 & 10. x is a negative and equal to the # of places the decimal point moved. Represent each of the following in scientific notation, showing only significant digits. 1, ,213, Rounding Rules Let x be defined as the number to be dropped. There are three scenarios The preceding number remains the same. The preceding number is increased by one unit. If the preceding number is even keep number the same. odd increase number by one unit. Check your notes! This is a special case Round off the following to three significant figures. 1, ,894,

5 Significant Figures and Algebraic Operations: Addition & Subtraction Given the following measurements, report the sum in the proper number of significant figures. least # decimal places in 1.2 in in The # of decimal places the sum must have is. How many sig figs does each measurement have? Hint: Lining up the decimal places vertically may be helpful in 1.2 in in in Given the measurements below, report the sum or difference in the proper number of significant figures. (2.096 g g) g = 12 L L L = Significant Figures and Algebraic Operations: Multiplication & Division Given the following measurements, report the quotient in the proper number of significant figures. least # sig figs mm 3.01 in 4.0 mm The # of significant figures the product must have is. Given the measurements below, report the quotient in the proper number of significant figures. (1.460 ml ml) ml = ( kg)( kg) / (0.258 kg) = Take Home Message: Your answer CANNOT be more precise than the least precise measurement! 5