This document discusses the rules for determining significant digits in measurements and calculations. It defines what makes a digit significant and provides examples to illustrate the rules. Significant digits indicate the precision or uncertainty in a measurement. The number of significant digits reported in a calculation must be consistent with and justified by the least precise measurement used. Rounding intermediate calculations can introduce inaccuracies into the final reported value. Practice problems are provided to help apply the rules for addition, subtraction, multiplication and division.

1. SIGNIFICANT DIGITS WATCH OUT!!!! CERTAIN RULES TOTAKECARE FIND RULES AND EXERCISES ABOUT SIGNIFICANT DIGITS, BESIDES THE BIG IMPORTANCE THEY HAVE IN SCIENCE AND ENGINEERING……. Andrea Ordoñez Carvajal

2. WHAT ARE SIGNIFICANT DIGITS?? The number of significant digits in an answer to a calculation will depend on the number of significant digits in the given data, as discussed in the next rules. Approximate calculations (order-of-magnitude estimates) always result in answers with only one or two significant digits. Source: www.teacherspayteachers.com

3. When are Digits Significant? RULES Non-zero digits are always significant. Thus, 22 has two significant digits, and 22.3 has three significant digits. 0

4. When are Digits Significant? RULES With zeroes, the situation is more complicated: Zeroes placed before other digits are not significant; 0.046 has two significant digits. Zeroes placed between other digits are always significant; 4009 kg has four significant digits. Zeroes placed after other digits but behind a decimal point are significant; 7.90 has three significant digits.

5. When are Digits Significant? RULES Zeroes at the end of a number are significant only if they are behind a decimal point as in (c). Otherwise, it is impossible to tell if they are significant. For example, in the number 8200, it is not clear if the zeroes are significant or not. The number of significant digits in 8200 is at least two, but could be three or four. To avoid uncertainty, use scientific notation to place significant zeroes behind a decimal point: 8.200 ´ 103 has four significant digits 8.20 ´ 103 has three significant digits 8.2 ´ 103 has two significant digits

6. Significant Digits in Multiplication, Division, Trig. functions, etc. In a calculation involving multiplication, division, trigonometric functions, etc., the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied, divided etc.

7. Significant Digits in Addition and Subtraction When quantities are being added or subtracted, the number 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.

8. SOME EXAMPLES!! 3.14159 has six significant digits (all the numbers give you useful information) 1000 has one significant digit (only the 1 is interesting; you don't know anything for sure about the hundreds, tens, or units places; the zeroes may just be placeholders; they may have rounded something off to get this value) 1000.0 has five significant digits (the ".0" tells us something interesting about the presumed accuracy of the measurement being made: that the measurement is accurate to the tenths place, but that there happen to be zero tenths) 0.00035 has two significant digits (only the 3 and 5 tell us something; the other zeroes are placeholders, only providing information about relative size) 0.000350 has three significant digits (that last zero tells us that the measurement was made accurate to that last digit, which just happened to have a value of zero)

9. The Two Greatest Sins Regarding Significant Digits Writing more digits in an answer (intermediate or final) than justified by the number of digits in the data. Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.

10. MAKE THIS ON YOUR OWN!! ekt = ?, where k = 0.0189 yr-1, and t = 25 yr. ab/c = ?, where a = 483 J, b = 73.67 J, and c = 15.67 x + y + z = ?, where x = 48.1, y = 77, and z = 65.789 m - n - p = ?, where m = 25.6, n = 21.1, and p = 2.43

11. SOURCE http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm http://www.purplemath.com/modules/rounding2.htm “The major problem with all of us is we don't continue what we start” Sentence for success