Significant Figures General Chemistry

What are Significant Figures? Digits in a measured quantity that indicate the precision of the measurement. All measuring devices are not created equal, some are more precise than others.

Counting Significant Figures All non-zero numbers are counted. Only some zeros are counted, DO NOT count the following zeros: Consecutive zeros at the END of a number greater than one WITHOUT a written decimal. (e.g. 3000; 70) Zero in front of decimal in a number less than one. (e.g. 0.897) Place-holder zeros.

Place-Holder Zeros Found in numbers less than one. They are right of the decimal, but left of the first non-zero digit. 0.00754

Simple Rules: If the number is greater than one, with NO written decimal, never count consecutive zeros at the END. If the number is less than one, never count consecutive zeros at the BEGINNING.

Scientific Notation: Since proper scientific notation has a leading number greater than or equal to one with a written decimal, all digits are counted. Example: 2.3 x 107 has 2 sig. figs. 5.007 x 10-3 has 4 sig. figs.

Let’s Practice!! 74030 4 74030 30.020 5 30.020 0.1250 4 0.1250 0.0087020 5 0.0087020 2 30. 30. 500 500 1 0.0907 0.0907 3

Multiplying with Significant Figures Determine the number of sig. figs. In each number. Answer must be rounded so it has the same number of sig. figs. as the number used with the LEAST Example: 2.3 x 5.98 = ? Calculator answer = 13.754 Correct answer = 14

Dividing with Significant Figures Same rule as multiplying! Example: 5.789/6.55 = ? Calculator answer = 0.88381679. . . Correct answer = 0.884 The first number has 4 sig. figs., the second has 3, so the answer is rounded to 3!

Adding with Significant Figures When adding numbers we do not concern ourselves with the number of sig. figs. in each of the measurements, but their PLACE VALUE instead. The answer is always rounded so it is reported to the LEAST PRECISE place. Example (See next slide.)

Example 5 + 3.14 + 2.8 = ? Calculator answer = 10.94 Correct answer = 11 The number 5 is only reported to the ONES place; therefore, the answer is rounded to the ones place!

Subtracting with Significant Figures Same rule as Adding!