Significant Digits Measurements

Description and Measurement  Key Vocabulary  Precision  Accuracy

Description and Measurement  Precision- how close measurements are to one another  Example: If you measure the width of a floor tile several times and you get: 1.0m, 1.1m, 1.0m, and 1.0m; then your results are precise

Description and Measurement  Accuracy- comparison of a measurement to an accepted value  Example: when an archer shoots and arrow and hits the bullseye, the archer is accurate

Description and Measurement

 Significant Figures- you can only be as precise as your least precise measurement  Digits other than zero (0) are always significant  Zeros after a decimal point are significant  Zeros between any other digit are significant  Initial zeros are not significant  Zeros at the end of a whole number may or may not be significant  Depends on if you place a decimal after the zero

Description and Measurements  How many significant figures in these examples  seconds  meters  350 kilometers  5.00 milliliters  450. grams

Description and Measurements  There are also rules to follow when deciding the number of significant digits in the answer to a calculation.  It depends on the type of calculation that you are doing.

Multiplying and Dividing with Significant Digits  The rule for multiplication and division is to look at the total number of significant digits in all of the numbers involved in the calculation.  The rule for multiplication and division is to look at the total number of significant digits in all of the numbers involved in the calculation.  Then, decide what is the smallest number of significant figures you are working with in the problem.  Then, decide what is the smallest number of significant figures you are working with in the problem.

Example  1.35/17=  How many SD’s are in each number?  1.35?  17?

 Significant Digits  Significant Digits  2 is the smallest number of SD’s, so our answer will have no more than 2 Significant Digits.  rounded to 2 SD’s= 0.079

Adding and Subtracting with Significant Digits  The # of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.

Example 5.67 J (two decimal places) J (one decimal place) J (four decimal place) 7.7 J (one decimal place)

Quick Review  Would the sum of 5.7 and 6.2 need to be rounded? Why or why not?  Would the sum of 3.28 and 4.1 need to be rounded? Why or why not?

Quick Review  Solve these problems using the correct number of significant figures:  =  =  =  =  180 / =  / 40=  x 35.6=  6.3 x 20 x 30=