Read the following texts and table with financial data from an S&P 500 earnings report carefully.Based on the question-answer history (if provided), answer the last question. The answer may require mathematical calculation based on the data provided.


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 . <table class='wikitable'><tr><td>1</td><td>( amounts in millions )</td><td>2012</td><td>2011</td><td>2010</td></tr><tr><td>2</td><td>unrecognized tax benefits at beginning of year</td><td>$ 11.0</td><td>$ 11.1</td><td>$ 17.5</td></tr><tr><td>3</td><td>gross increases 2013 tax positions in prior periods</td><td>0.7</td><td>0.5</td><td>0.6</td></tr><tr><td>4</td><td>gross decreases 2013 tax positions in prior periods</td><td>-4.9 ( 4.9 )</td><td>-0.4 ( 0.4 )</td><td>-0.4 ( 0.4 )</td></tr><tr><td>5</td><td>gross increases 2013 tax positions in the current period</td><td>1.2</td><td>2.8</td><td>3.1</td></tr><tr><td>6</td><td>settlements with taxing authorities</td><td>2013</td><td>-1.2 ( 1.2 )</td><td>-9.5 ( 9.5 )</td></tr><tr><td>7</td><td>increase related to acquired business</td><td>2013</td><td>2013</td><td>0.4</td></tr><tr><td>8</td><td>lapsing of statutes of limitations</td><td>-1.2 ( 1.2 )</td><td>-1.8 ( 1.8 )</td><td>-0.6 ( 0.6 )</td></tr><tr><td>9</td><td>unrecognized tax benefits at end of year</td><td>$ 6.8</td><td>$ 11.0</td><td>$ 11.1</td></tr></table> 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: what is the balance of unrecognized tax benefits at end of year 2012?
Answer: 6.8
Question: what about 2011?
Answer: 11.0
Question: what is the sum for these two years?
Answer: 17.8
Question: what about the sum including 2010?
Answer: 28.9
Question: what is the average for these three years?

9.63333