tax benefits recognized for stock-based compensation during the years ended december 31 , 2011 , 2010 and 2009 , were $ 16 million , $ 6 million and $ 5 million , respectively . the amount of northrop grumman shares issued before the spin-off to satisfy stock-based compensation awards are recorded by northrop grumman and , accordingly , are not reflected in hii 2019s consolidated financial statements . the company realized tax benefits during the year ended december 31 , 2011 , of $ 2 million from the exercise of stock options and $ 10 million from the issuance of stock in settlement of rpsrs and rsrs . unrecognized compensation expense at december 31 , 2011 there was $ 1 million of unrecognized compensation expense related to unvested stock option awards , which will be recognized over a weighted average period of 1.1 years . in addition , at december 31 , 2011 , there was $ 19 million of unrecognized compensation expense associated with the 2011 rsrs , which will be recognized over a period of 2.2 years ; $ 10 million of unrecognized compensation expense associated with the rpsrs converted as part of the spin-off , which will be recognized over a weighted average period of one year ; and $ 18 million of unrecognized compensation expense associated with the 2011 rpsrs which will be recognized over a period of 2.0 years . stock options the compensation expense for the outstanding converted stock options was determined at the time of grant by northrop grumman . there were no additional options granted during the year ended december 31 , 2011 . the fair value of the stock option awards is expensed on a straight-line basis over the vesting period of the options . the fair value of each of the stock option award was estimated on the date of grant using a black-scholes option pricing model based on the following assumptions : dividend yield 2014the dividend yield was based on northrop grumman 2019s historical dividend yield level . volatility 2014expected volatility was based on the average of the implied volatility from traded options and the historical volatility of northrop grumman 2019s stock . risk-free interest rate 2014the risk-free rate for periods within the contractual life of the stock option award was based on the yield curve of a zero-coupon u.s . treasury bond on the date the award was granted with a maturity equal to the expected term of the award . expected term 2014the expected term of awards granted was derived from historical experience and represents the period of time that awards granted are expected to be outstanding . a stratification of expected terms based on employee populations ( executive and non-executive ) was considered in the analysis . the following significant weighted-average assumptions were used to value stock options granted during the years ended december 31 , 2010 and 2009: .

Table:
 | 2010 | 2009
dividend yield | 2.9% ( 2.9 % ) | 3.6% ( 3.6 % )
volatility rate | 25% ( 25 % ) | 25% ( 25 % )
risk-free interest rate | 2.3% ( 2.3 % ) | 1.7% ( 1.7 % )
expected option life ( years ) | 6 | 5 & 6
the weighted-average grant date fair value of stock options granted during the years ended december 31 , 2010 and 2009 , was $ 11 and $ 7 , per share , respectively. .

Question: at december 312011 what was the ratio of the unrecognized compensation expense associated of rsrs to the rpsrs
Answer: 1.9
Calculation: divide(19, const_10)