a valuation allowance totaling $ 43.9 million , $ 40.4 million and $ 40.1 million as of 2012 , 2011 and 2010 year end , respectively , has been established for deferred income tax assets primarily related to certain subsidiary loss carryforwards that may not be realized . realization of the net deferred income tax assets is dependent on generating sufficient taxable income prior to their expiration . although realization is not assured , management believes it is more- likely-than-not that the net deferred income tax assets will be realized . the amount of the net deferred income tax assets considered realizable , however , could change in the near term if estimates of future taxable income during the carryforward period fluctuate . the following is a reconciliation of the beginning and ending amounts of unrecognized tax benefits for 2012 , 2011 and ( amounts in millions ) 2012 2011 2010 .

2012: unrecognized tax benefits at beginning of year: 11
gross increases 2013 tax positions in prior periods: 0.7
gross decreases 2013 tax positions in prior periods: -4.9
gross increases 2013 tax positions in the current period: 1.2
settlements with taxing authorities: 2013
increase related to acquired business: 2013
lapsing of statutes of limitations: -1.2
unrecognized tax benefits at end of year: 6.8
2011: unrecognized tax benefits at beginning of year: 11.1
gross increases 2013 tax positions in prior periods: 0.5
gross decreases 2013 tax positions in prior periods: -0.4
gross increases 2013 tax positions in the current period: 2.8
settlements with taxing authorities: -1.2
increase related to acquired business: 2013
lapsing of statutes of limitations: -1.8
unrecognized tax benefits at end of year: 11
2010: unrecognized tax benefits at beginning of year: 17.5
gross increases 2013 tax positions in prior periods: 0.6
gross decreases 2013 tax positions in prior periods: -0.4
gross increases 2013 tax positions in the current period: 3.1
settlements with taxing authorities: -9.5
increase related to acquired business: 0.4
lapsing of statutes of limitations: -0.6
unrecognized tax benefits at end of year: 11.1

of the $ 6.8 million , $ 11.0 million and $ 11.1 million of unrecognized tax benefits as of 2012 , 2011 and 2010 year end , respectively , approximately $ 4.1 million , $ 9.1 million and $ 11.1 million , respectively , would impact the effective income tax rate if recognized . interest and penalties related to unrecognized tax benefits are recorded in income tax expense . during 2012 and 2011 , the company reversed a net $ 0.5 million and $ 1.4 million , respectively , of interest and penalties to income associated with unrecognized tax benefits . as of 2012 , 2011 and 2010 year end , the company has provided for $ 1.6 million , $ 1.6 million and $ 2.8 million , respectively , of accrued interest and penalties related to unrecognized tax benefits . the unrecognized tax benefits and related accrued interest and penalties are included in 201cother long-term liabilities 201d on the accompanying consolidated balance sheets . snap-on and its subsidiaries file income tax returns in the united states and in various state , local and foreign jurisdictions . it is reasonably possible that certain unrecognized tax benefits may either be settled with taxing authorities or the statutes of limitations for such items may lapse within the next 12 months , causing snap-on 2019s gross unrecognized tax benefits to decrease by a range of zero to $ 2.4 million . over the next 12 months , snap-on anticipates taking uncertain tax positions on various tax returns for which the related tax benefit does not meet the recognition threshold . accordingly , snap-on 2019s gross unrecognized tax benefits may increase by a range of zero to $ 1.6 million over the next 12 months for uncertain tax positions expected to be taken in future tax filings . with few exceptions , snap-on is no longer subject to u.s . federal and state/local income tax examinations by tax authorities for years prior to 2008 , and snap-on is no longer subject to non-u.s . income tax examinations by tax authorities for years prior to 2006 . the undistributed earnings of all non-u.s . subsidiaries totaled $ 492.2 million , $ 416.4 million and $ 386.5 million as of 2012 , 2011 and 2010 year end , respectively . snap-on has not provided any deferred taxes on these undistributed earnings as it considers the undistributed earnings to be permanently invested . determination of the amount of unrecognized deferred income tax liability related to these earnings is not practicable . 2012 annual report 83 .

Questions:
what is the balance of unrecognized tax benefits at end of year 2012?
what about 2011?
what is the sum for these two years?
what about the sum including 2010?
what is the average for these three years?

Answers:
6.8
11.0
17.8
28.9
9.63