WHAT IS A SIGNIFICANT FIGURE? When you are making a measurement there are always a certain number of known or certain digits. Then as part of the measurement there will always be a digit that is uncertain because it is your guess. The known or certain digits plus the first unknown Digit is referred to as the SIGNIFICANT FIGURES Kenneth E. Schnobrich

PRECISION vs ACCURACY PRECISION: this refers to a situation where the same result is gotten each time you perform the operation • repeatedly hitting the same spot in darts ACCURACY: this refers to how close you come to the accepted value or result • how close you are to the bullseye

SIGNIFICANT FIGURES The following rules apply to significant figures: All digits in a measurement are considered significant Zeros that fall between digits are considered significant Zeros to the right of a decimal and to the right of a non-zero are considered significant If a decimal point is placed after a zero all of the intervening zeros are significant Zeros after a digit but not followed by a decimal are not significant

EXACT NUMBERS These are usually numbers that are obtained by counting rather than using a measuring device such as a buret or graduated cylinder - 12 eggs in dozen, 2 socks in a pair, 144 in a gross © Kenneth E. Schnobrich

SIGNIFICANT FIGURES Working with Significant figures: When you add or subtract numbers: the final answer can have no more decimal places than the least precise value in the operation 2. When you multiply or divide numbers: the final answer can have no more significant figures than the smallest number of significant figures in the operation

EXAMPLES ADDING & SUBTRACTING: 5.0043 4.032 1.02 3.2 5.0043 1.02 4.02 13.3

EXAMPLES Multiplying and Dividing 4.91 5.0043 4.032 1.02 5.0043 20.33

MORE EXAMPLES How many Significant figures in each of the following: 1. 0.0043 2. 1.0043 3. 14300 4. 5820. 5. 30089 6. 2.0607

MORE EXAMPLES How many Significant figures in each of the following: 2. 1.0043 + 2.08 = 3. 14300/4 = 4. 5820. x 4.32 = 5. 30089 - 7.32 = 6. 2.0607 + 3.85 =

ROUNDING When rounding use only the first digit to the right of the last significant figure . 4.348 becomes 4.3 if rounded to 2 sig.figs. Rules: In a series of calculations, carry the extra digits through to the final result, then round. If the digit to be removed Is less than 5 the preceding digit stays the same. 1.33 becomes 1.3 Is equal to or greater than 5, the preceding digit is increased by 1. 1.36 becomes 1.4