{"pre_text": ["republic services , inc .", "notes to consolidated financial statements 2014 ( continued ) in december 2008 , the board of directors amended and restated the republic services , inc .", "2006 incentive stock plan ( formerly known as the allied waste industries , inc .", "2006 incentive stock plan ( the 2006 plan ) ) .", "allied 2019s shareholders approved the 2006 plan in may 2006 .", "the 2006 plan was amended and restated in december 2008 to reflect republic as the new sponsor of the plan , and that any references to shares of common stock are to shares of common stock of republic , and to adjust outstanding awards and the number of shares available under the plan to reflect the allied acquisition .", "the 2006 plan , as amended and restated , provided for the grant of non- qualified stock options , incentive stock options , shares of restricted stock , shares of phantom stock , stock bonuses , restricted stock units , stock appreciation rights , performance awards , dividend equivalents , cash awards , or other stock-based awards .", "awards granted under the 2006 plan prior to december 5 , 2008 became fully vested and nonforfeitable upon the closing of the allied acquisition .", "no further awards will be made under the 2006 stock options we use a lattice binomial option-pricing model to value our stock option grants .", "we recognize compensation expense on a straight-line basis over the requisite service period for each separately vesting portion of the award , or to the employee 2019s retirement eligible date , if earlier .", "expected volatility is based on the weighted average of the most recent one year volatility and a historical rolling average volatility of our stock over the expected life of the option .", "the risk-free interest rate is based on federal reserve rates in effect for bonds with maturity dates equal to the expected term of the option .", "we use historical data to estimate future option exercises , forfeitures ( at 3.0% ( 3.0 % ) for each of the periods presented ) and expected life of the options .", "when appropriate , separate groups of employees that have similar historical exercise behavior are considered separately for valuation purposes .", "the weighted-average estimated fair values of stock options granted during the years ended december 31 , 2014 , 2013 and 2012 were $ 5.74 , $ 5.27 and $ 4.77 per option , respectively , which were calculated using the following weighted-average assumptions: ."], "post_text": ["."], "table": [["", "2014", "2013", "2012"], ["expected volatility", "27.5% ( 27.5 % )", "28.9% ( 28.9 % )", "27.8% ( 27.8 % )"], ["risk-free interest rate", "1.4% ( 1.4 % )", "0.7% ( 0.7 % )", "0.8% ( 0.8 % )"], ["dividend yield", "3.2% ( 3.2 % )", "3.2% ( 3.2 % )", "3.2% ( 3.2 % )"], ["expected life ( in years )", "4.6", "4.5", "4.5"], ["contractual life ( in years )", "7.0", "7.0", "7.0"]], "table_ori": [["", "2014", "2013", "2012"], ["Expected volatility", "27.5%", "28.9%", "27.8%"], ["Risk-free interest rate", "1.4%", "0.7%", "0.8%"], ["Dividend yield", "3.2%", "3.2%", "3.2%"], ["Expected life (in years)", "4.6", "4.5", "4.5"], ["Contractual life (in years)", "7.0", "7.0", "7.0"]]}

Question: what was the percentage change in the expected volatility from 2012 to 2013
Evidence:
table_1: the expected volatility of 2014 is 27.5% ( 27.5 % ) ; the expected volatility of 2013 is 28.9% ( 28.9 % ) ; the expected volatility of 2012 is 27.8% ( 27.8 % ) ;
Program: subtract(28.9, 27.8), divide(#0, 27.8)
Answer:
str_answer: 3.95%
exe_answer: 0.03957