Significant Figures and Rounding

Significant Figures Significant figures - show accuracy in measurements & calculations Significant figures in a measurement consist of all of the digits known with certainty plus one digit that is an estimate. The number of significant figures in a measurement indicates to precision in the measurement it is. A balance that reads to the 1.0 gram is less certain in a measurement that a balance that reads to 1.000 grams.

Rules for Identifying sig. figs. In a Measurement The digits 1 through 9 ( all non-zero digits) are ALWAYS significant. 243 Has 3 significant figures 1.287 Four significant figures How many significant figures are in 142.32 5 Significant digits How many significant figures are in 3.1 2 significant digits

Rules for Identifying sig. figs. In a Measurement Middle zeros are ALWAYS significant figures (zeros between non-zero digits) 207 Three significant figures 1.0032 Five significant figures How many significant figures are in 207.5 4 significant digits How many significant figures are in 60,007 5 significant digits

Rules for Identifying sig. figs. In a Measurement Leading zeros are NEVER significant. Leading zeros are zeros that occur at the beginning of a number. Leading zeros function to indicate the position of the decimal point. 0.0045 Two significant figures 0.034009 Five significant figures How many significant figures are in 0.0307 3 significant digits How many significant figures are in 0.0037009 5 significant digits

Rules for Identifying sig. figs. In a Measurement Ending zeros are zeros at the end of the number. They are SOMETIMES significant. They ARE significant if there is a decimal point anywhere in the number. If no decimal point, ending zeros are NOT significant. 200.0 Four significant figures 2000. Four significant figures 200 One significant figure How many significant figures are in 62.00 4 significant digits How many significant figures are in 24.70 How many significant figures are in 360,000 2 significant digits

The do not affect the number of sig figs in your final answer Counting, exact and defined numbers have an infinite number of significant figures. Pi- 3.1415926535893238……… Avogadro’s number- 6.0221415 x 10^23 A bakers dozen The do not affect the number of sig figs in your final answer

EXERCISE 1 10423 10423 5 sig figs 1230.0 1230.0 5 sig figs 150 0.0032 0.0032 2 sig figs 3300 3300 2 sig figs 10.0 10.0 3 sig figs 0.05010 0.05010 4 sig figs

Rounding Rounding is the process of deleting extra digits from a calculated number. 1. If the first digit to be dropped is less than 5, that digit and all the digits that follow it are simply dropped. 1.673 rounded to three significant figures becomes 1.67 2.If the first digit to be dropped is greater than or equal to 5, the excess digits are all dropped and the last significant figure is rounded up. 62.873 rounded to three significant figures becomes 62.9

Round The following 423.78 to three significant figures 424 B. 0.000123 to two significant figures 0.00012 C. 22.550 to four significant figures 22.55 D. 129.6 to three significant figures 130. (must have decimal) E. 0.365 to one significant figure 0.4 F. 7.206 to three significant figures 7.21

Calculations Using Significant Figures A calculated number cannot be more precise than the data numbers used to calculate it. In other words: the answer can’t be more precise than any of the original numbers in the problem.

Addition and Subtraction *Two different rules apply: The Rule for Addition & Subtraction is DIFFERENT than the Rule for Multiplication and Division   1. Addition & Subtraction In addition and subtraction, the last digit in the answer must be expressed to the same decimal place value as the entry with the ____least________ accurate decimal position. 5.72 (accurate to the hundredths position) 0.00648 (accurate to the hundred thousandths position) 37.916__ (accurate to the thousandths position) 43.7008 Becomes 43.70 to the hundredths position 78.4 (accurate to the tenths position) -3.628 (accurate to the thousandths position) 74.772 Becomes 74.8 to the tenths position l

Addition and Subtraction *Write the given calculated answer in the correct number of significant figures. Look at decimal places only   a. 3.64 + 0.0829 = 3.7229 3.72 67.4 + 4.28 = 71.68 71.7 3.289 – 0.66 = 2.629 2.63 5.976 – 0.497 = 5.497 no change 269 + 3.27 + 4.6 = 276.87 no decimal place in first number 277 7.2 + 0.69 – 0.0324 = 7.8666 7.9

Multiplication and Division In multiplication and division the number of significant figures in the product or quotient must be the same as in the number in the calculation that contains the least significant figures This is the rule we mainly use!!!

6.038 x 2.57 = 15.51766 Correct answer is 15.5 because the three significant digits in 2.57 limits our answers to three significant digits 120.0 ÷ 4.000 = 30 Correct answer is 30.00 because each entry has four significant digits so your answer must have four significant digits. (3.130 x 3.14) ÷ 3.1 = 3.170387097 Correct answer is 3.2 because the least number of significant digits in the entries is two so our answer must only have two significant digits.

Multiplication and Division Practice Count total number of Sig Figs!!!! . 3.751 x 0.42 = 1.57542 1.6 6.7321 x 0.0021 = 0.01420041 0.014 3.27 / 4.6 = 0.710869565 0.71 49.7 / 0.05976 = 831.6599732 832 (7.2 x 0.69) / 3.24 = 0.866666666 0.87 269 / (3.270 x 4.6) = 17.88323602 18