{"pre_text": ["republic services , inc .", "notes to consolidated financial statements 2014 ( continued ) the plan to reflect the allied acquisition .", "the 2006 plan , as amended and restated , provides 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 acquisition .", "awards may be granted under the 2006 plan , as amended and restated , after december 5 , 2008 only to employees and consultants of allied and its subsidiaries who were not employed by republic prior to such date .", "as of december 31 , 2013 , there were approximately 15.6 million shares of common stock reserved for future grants under the 2006 plan .", "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 , 2013 , 2012 and 2011 were $ 5.27 , $ 4.77 and $ 5.35 per option , respectively , which were calculated using the following weighted-average assumptions: ."], "post_text": ["."], "table": [["", "2013", "2012", "2011"], ["expected volatility", "28.9% ( 28.9 % )", "27.8% ( 27.8 % )", "27.3% ( 27.3 % )"], ["risk-free interest rate", "0.7% ( 0.7 % )", "0.8% ( 0.8 % )", "1.7% ( 1.7 % )"], ["dividend yield", "3.2% ( 3.2 % )", "3.2% ( 3.2 % )", "2.7% ( 2.7 % )"], ["expected life ( in years )", "4.5", "4.5", "4.4"], ["contractual life ( in years )", "7.0", "7.0", "7.0"]], "table_ori": [["", "2013", "2012", "2011"], ["Expected volatility", "28.9%", "27.8%", "27.3%"], ["Risk-free interest rate", "0.7%", "0.8%", "1.7%"], ["Dividend yield", "3.2%", "3.2%", "2.7%"], ["Expected life (in years)", "4.5", "4.5", "4.4"], ["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 2013 is 28.9% ( 28.9 % ) ; the expected volatility of 2012 is 27.8% ( 27.8 % ) ; the expected volatility of 2011 is 27.3% ( 27.3 % ) ;
Program: subtract(28.9, 27.8), divide(#0, 27.8)
Answer:
str_answer: 3.95%
exe_answer: 0.03957