Significant Figures (Digits) u Exact numbers – pure number/significant digits are NOT applicable u Examples of exact numbers - 10 pennies - 30 students - 1 dozen %

Significant Figures (Digits) u Significant Digits – a number that is part of a measured quantity. Significant digits only apply to measurements. u Some examples of significant digits - 15 cm in qt

Significant Figures (Digits) u Rules for using significant digits 1. Apply only to measured quantities 2. Must include units 3. Must reflect the precision of the measuring device.

Significant Figures (Digits) u Significant digits apply only to MEASURED quantities a. length b. volume c. mass/weight

Significant Figures (Digits) u All non-zero digits are significant a. 531 contains 3 significant digits b contains 4 significant digits c. 4 contains 1 significant digit

Significant Figures (Digits) u Zeros BETWEEN non-zero digits are significant a. 101 contains 3 significant digits b contains 5 significant digits

Significant Figures (Digits) u Trailing zeros are NOT significant a. 10 contains 1 significant digit b contains 3 significant digits c contains 1 significant digit

Significant Figures (Digits) u Trailing zeros are NOT significant a. 10 contains 1 significant digit b contains 3 significant digits c contains 1 significant digit u UNLESS there is a decimal point! a. 10. contains 2 significant digits b contains 4 significant digits c contains 5 significant digits

Significant Figures (Digits) u Zeros AFTER a decimal point are significant a contains 3 significant digits b contains 6 significant digits

Significant Figures (Digits) u Zeros AFTER a decimal point are significant a contains 3 significant digits b contains 6 significant digits u UNLESS the function of the zero is to locate the decimal point a contains 1 significant digits b contains 2 significant digits

Significant Figures (Digits) u Zeros AFTER a decimal point and AFTER a significant digit are significant a contains 2 significant digits b contains 3 significant digits c contains 5 significant digits

Significant Figures (Digits) u Non-zero digits BEFORE a decimal point makes all zeros significant a contains 3 significant digits b contains 4 significant digits c contains 7 significant digits

Significant Figures (Digits) u Significant digits do not apply to counting numbers or exact numbers a. 47 people - counting number b. 63 cars entered the race – counting number c. 10 pennies = 1 dime exact number d. 12 apples = 1 dozen

Significant Figures (Digits) u Adding with significant digits: cm cm cm The answer to this addition can contain only 2 digits beyond the decimal point. The answer to this problem is cm, a result based on rounding.

Significant Figures (Digits) u Rounding - rounding is the last step in completing a problem and expressing the answer with the correct number of significant digits. Note: Never round until the last step/the final answer.

Significant Figures (Digits) u Rules for Rounding u If the rounding digit is greater than 5, increase the preceding digit by 1 u If the rounding digit is less than 5, leave the preceding digit alone u If the rounding digit is 5, then make the preceding digit EVEN!

Significant Figures (Digits) u Multiplying with significant digits: cm x cm cm 2 The answer to this multiplication can contain only 4 significant digits. Therefore, the answer to this problem is cm.

Significant Figures (Digits) u Round cm to 2 significant digits

Significant Figures (Digits) u Round cm to 2 significant digits u The answer is 48 cm or better 48.cm u Now, round cm to 3 significant digits

Significant Figures (Digits) u Round cm to 2 significant digits u The answer is 48 cm or better 48. cm u Now, round cm to 3 significant digits u The answer is 47.8 cm u Now, round to 4 significant digits

Significant Figures (Digits) u Round cm to 2 significant digits u The answer is 48 cm or better 48. cm u Now, round cm to 3 significant digits u The answer is 47.8 cm u Now, round cm to 4 significant digits u The answer is cm u Finally, round to 5 significant digits

Significant Figures (Digits) u Round cm to 2 significant digits u The answer is 48 cm or better 48. cm u Now, round cm to 3 significant digits u The answer is 47.8 cm u Now, round to 4 significant digits u The answer is cm u Finally, round cm to 5 significant digits u The answer is cm

Significant Figures (Digits) u Round to one significant digit

Significant Figures (Digits) u Round g to one significant digit u The answer is 0.09 g u Now, round g to three significant digits

Significant Figures (Digits) u Round g to one significant digit u The answer is 0.09 g u Now, round g to three significant digits u The answer is g u Now, round g to four significant digits

Significant Figures (Digits) u Round g to one significant digit u The answer is 0.09 g u Now, round g to three significant digits u The answer is g u Now, round g to four significant digits u The answer is g

Exponential Notation u Sometimes we deal with very large or very small numbers. It is difficult to write these numbers with all of the necessary zeros just to show where the decimal point should be. Instead we have developed a technique which allows us to write these numbers in a form which easily shows the number of significant digits and the location of the decimal point. The technique is call exponential notation or scientific notation.

Scientific Notation u Scientific Notation (Exponential Notation) writes all numbers using this format: D.DD x 10 p u D represents the significant digits. Note that only one digit remains to the LEFT of the decimal point. The remaining significant digits appear to the right of the decimal point. u P, the power of the base 10, represents the number of spaces that the decimal point had to be moved.

Scientific Notation u Write 9600 in scientific notation. u First, determine the number of significant digits in the number. In this case there are two (2). u Since there is no decimal point in this number, place a decimal point at the end of the number: u Now, move the decimal point to the LEFT until there is only a single digit to the left of the decimal point.

Scientific Notation u Now, move the decimal point to the LEFT until there is only a single digit to the left of the decimal point. u The result is: 9.600; since the result should have 2 significant digits, we write the first part as: 9.6 x 10 p u What is the value for p? There are two items that must be considered to determine the value of p. What are they?

Scientific Notation u What is the value for p? There are two items that must be considered to determine the value of p. What are they? u (1) How many spaces was the decimal point moved? In our example the answer is 3. u (2) In which direction, Right (-) or Left (+), was the decimal point moved? In our case it was moved to the LEFT. The sign will be +.

Scientific Notation u The final notation for our example will be: 9.6 x 10 3 u Write in scientific notation.

Scientific Notation u Write in scientific notation. u There are 3 significant digits in this number. u Move the decimal point three spaces. u The result is: 6.02 x 10 -3

Unit Factors Conversion Factors Used to convert from one unit to another unit in the same measuring system or a different measuring system Use the “from” and “to” method to determine the values to be placed in the conversion factor

Unit Factors 100 cm  1 meter This is an EXACT number - there are exactly 100 cm in 1 meter by definition; the rules for significant digits do not apply Practice using conversion/unit factors

Unit Factors