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 .

<i>(Amounts in millions)</i>
2012
2011
2010
Unrecognized tax benefits at beginning of year
$11.0
$11.1
$17.5
Gross increases – tax positions in prior periods
0.7
0.5
0.6
Gross decreases – tax positions in prior periods
(4.9)
(0.4)
(0.4)
Gross increases – tax positions in the current period
1.2
2.8
3.1
Settlements with taxing authorities
–
(1.2)
(9.5)
Increase related to acquired business
–
–
0.4
Lapsing of statutes of limitations
(1.2)
(1.8)
(0.6)
Unrecognized tax benefits at end of year
$6.8
$11.0
$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 .

Question: Analyse this data from a financial earnings document. what was the average unrecognized tax benefits at end of year from 2010 to 2012
Choices:
0.00001
9.63333
6.86667
12.63333
7.4
Correct choice index: 1