REPUBLIC SERVICES, INC.  AND SUBSIDIARIES NOTES TO CONSOLIDATED FINANCIAL STATEMENTS The components of the net deferred income tax asset and liability at December 31, 2008 and 2007 are as follows (in millions):
## Table 0 ##
(1) Certain amounts above have been reclassified to conform to the current year’s presentation.
We believe that it is more likely than not that the benefit from certain state net operating loss carryforwards will not be realized.
In recognition of this risk, we have provided a valuation allowance of $156.4 million on deferred tax assets relating to these state net operating loss carryforwards.
In assessing the realizability of deferred tax assets, management considers whether it is more likely than not that some portion or all of the deferred tax assets will not be realized after the initial recognition of the deferred tax asset.
We provide valuation allowances, as needed, to offset portions of deferred tax assets due to uncertainty surrounding the future realization of such deferred tax assets.
We adjust the valuation allowance in the period management determines it is more likely than not that deferred tax assets will or will not be realized.
We have recorded $107.1 million of deferred tax assets and $774.1 million of deferred income taxes and other long-term tax liabilities as part of our preliminary purchase price allocation for our acquisition of Allied.
This allocation is subject to change until we finalize our valuations and other estimates in 2009.
During the year ended December 31, 2008, we recorded a tax charge of $12.3 million related to nondeductible compensation payouts as a result of the merger with Allied.
During the year ended December 31, 2007, we recorded a net tax benefit of $4.8 million in our provision for income taxes related to the resolution of various tax matters, including the effective completion of the Internal Revenue Service (IRS) audits of our consolidated tax returns for fiscal years 2001 through 2004.
Income tax expense for the year ended December 31, 2006 includes a $5.1 million benefit related to the resolution of various income tax matters, including the effective completion of IRS audits for the years 1998 through 2000.
We made income tax payments (net of refunds received) of approximately $128.3 million, $151.9 million and $198.8 million for the years ended December 31, 2008, 2007 and 2006, respectively.
During 2008, approximately $32.0 million of federal tax payments have been deferred until February 2009 as a result of the merger with Allied.
Approximately $83.0 million of income taxes paid during the year ended December 31, 2006 related to fiscal 2005.
This $83.0 million payment had been deferred as a result of an IRS notice issued in response to Hurricane Katrina.
REPUBLIC SERVICES, INC.  AND SUBSIDIARIES NOTES TO CONSOLIDATED FINANCIAL STATEMENTS The following table shows our total reported revenue by service line for the respective years ended December 31 (in millions).
Intercompany revenue has been eliminated.
## Table 1 ##
15.
OTHER COMPREHENSIVE INCOME Fuel Hedges We have entered into multiple option agreements related to forecasted diesel fuel purchases.
Under SFAS 133, the options qualified for, and were designated as, effective hedges of changes in the prices of forecasted diesel fuel purchases (fuel hedges).
The following table summarizes our outstanding fuel hedges at December 31, 2008 and 2007:
## Table 2 ##
If the national U. S.  on-highway average price for a gallon of diesel fuel (average price) as published by the Department of Energy exceeds the contract price per gallon, we receive the difference between the average price and the contract price (multiplied by the notional gallons) from the counter-party.
If the national U. S.  on-highway average price for a gallon of diesel fuel is less than the contract price per gallon, we pay the difference to the counter-party.
The fair values of the fuel hedges are obtained from third-party counter-parties and are determined using standard option valuation models with assumptions about commodity prices being based on those observed in underlying markets (Level 2 in the fair value hierarchy).
The aggregated fair values of the outstanding fuel hedges at December 31, 2008 and 2007 were $11.7 million and $11.4 million, respectively, and have been recorded in other current liabilities and other current assets in our consolidated balance sheets, respectively.
In accordance with SFAS 133, the effective portions of the changes in fair values as of December 31, 2008 and 2007, net of tax, of $7.1 million and $6.9 million, respectively, have been recorded in stockholders’
REPUBLIC SERVICES, INC.  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS—(Continued) total notional value of $210.0 million, matured in August 2011.
This maturity was identical to our unsecured notes that also matured in August 2011.
Under the swap agreements, we paid interest at floating rates based on changes in LIBOR and received interest at a fixed rate of 6.75%.
We reduced interest expense by $5.4 million and $8.5 million due to periodic settlements of active swap agreements during years ended December 31, 2011 and 2010.
At December 31, 2012 and 2011 we had no interest rate swap agreements outstanding.
From time to time, we enter into treasury and interest rate locks to manage exposure to fluctuations in interest rates in anticipation of future debt issuances.
These transactions are accounted for as a cash flow hedges.
As of December 31, 2012 and 2011, no interest rate lock cash flow hedges were outstanding.
During the second quarter 2012, we entered into a number of interest rate lock agreements having an aggregate notional amount of $200.0 million with fixed interest rates approximating 2.20% to manage exposure to fluctuations in interest rates in anticipation of the planned issuance of the 3.550% Notes.
Upon issuance of the 3.550% Notes, we terminated the interest rate locks and paid $4.8 million to the counterparties.
The effective portion of the interest rate locks, recorded as a component of accumulated other comprehensive income, was $4.7 million, or $2.7 million net of tax.
During the first and second quarters of 2011, we entered into a number of interest rate lock agreements having an aggregate notional amount of $725.0 million with fixed interest rates ranging from 3.10% to 4.61% to manage exposure to fluctuations in interest rates in anticipation of the planned issuance of the 2011 Notes.
Upon issuance of the 2011 Notes, we terminated the interest rate locks and paid $36.5 million to the counterparties.
The effective portion of the interest rate locks, recorded as a component of accumulated other comprehensive income, was $36.2 million, or $21.2 million net of tax.
During the first quarter of 2010, we entered into interest rate lock agreements having an aggregate notional amount of $500.0 million to hedge interest rates in connection with the issuance of the 2010 Notes.
Upon issuance of these notes, we terminated the interest rate locks and paid approximately $7.0 million to the counterparties.
The effective portion of the interest rate locks, recorded as a component of accumulated other comprehensive income, was $6.4 million or $3.7 million net of tax.
As of December 31, 2012 and December 31, 2011, the effective portion of the interest rate locks, recorded as a component of accumulated other comprehensive income, was $24.6 million and $23.2 million, respectively.
The effective portion of the interest rate locks will be amortized as an adjustment to interest expense over the life of the issued debt using the effective interest rate method.
We expect to amortize $2.5 million over the next twelve months as a yield adjustment to our senior notes.
The effective portion of the interest rate locks amortized as a net increase to interest expense during the years ended December 31, 2012, 2011 and 2010 was $2.2 million, $1.4 million and $0.4 million, respectively.10.
INCOME TAXES The components of the provision for income taxes for the years ended December 31, are as follows:
## Table 3 ##
REPUBLIC SERVICES, INC.  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS—(Continued) high quality financial institutions.
Such balances may be in excess of FDIC insured limits.
To manage the related credit exposure, we continually monitor the credit worthiness of the financial institutions where we have deposits.
Concentrations of credit risk with respect to trade accounts receivable are limited due to the wide variety of customers and markets in which we provide services, as well as the dispersion of our operations across many geographic areas.
We provide services to commercial, industrial, municipal and residential customers in the United States and Puerto Rico.
We perform ongoing credit evaluations of our customers, but do not require collateral to support customer receivables.
We establish an allowance for doubtful accounts based on various factors including the credit risk of specific customers, age of receivables outstanding, historical trends, economic conditions and other information.
No customer exceeded 5% of our outstanding accounts receivable balance at December 31, 2012 and 2011.
Accounts Receivable, Net of Allowance for Doubtful Accounts Accounts receivable represent receivables from customers for collection, transfer, recycling, disposal and other services.
Our receivables are recorded when billed or when the related revenue is earned, if earlier, and represent claims against third parties that will be settled in cash.
The carrying value of our receivables, net of the allowance for doubtful accounts, represents their estimated net realizable value.
Provisions for doubtful accounts are evaluated on a monthly basis and are recorded based on our historical collection experience, the age of the receivables, specific customer information and economic conditions.
We also review outstanding balances on an account-specific basis.
In general, reserves are provided for accounts receivable in excess of ninety days old.
Past due receivable balances are written-off when our collection efforts have been unsuccessful in collecting amounts due.
The following table reflects the activity in our allowance for doubtful accounts for the years ended December 31, 2012, 2011 and 2010:
## Table 4 ##
Restricted Cash and Marketable Securities As of December 31, 2012, we had $164.2 million of restricted cash and marketable securities.
We obtain funds through the issuance of tax-exempt bonds for the purpose of financing qualifying expenditures at our landfills, transfer stations, collection and recycling centers.
The funds are deposited directly into trust accounts by the bonding authorities at the time of issuance.
As the use of these funds is contractually restricted, and we do not have the ability to use these funds for general operating purposes, they are classified as restricted cash and marketable securities in our consolidated balance sheets.
In the normal course of business, we may be required to provide financial assurance to governmental agencies and a variety of other entities in connection with municipal residential collection contracts, closure or postclosure of landfills, environmental remediation, environmental permits, and business licenses and permits as a financial guarantee of our performance.
At several of our landfills, we satisfy financial assurance requirements by depositing cash into restricted trust funds or escrow accounts.

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td>2008</td><td>2007 -1</td></tr><tr><td>Deferred tax liabilities relating to:</td><td></td><td></td></tr><tr><td>Difference between book and tax basis of property</td><td>$-1,257.9</td><td>$-544.5</td></tr><tr><td>Accruals currently deductible</td><td>-110.9</td><td>-92.0</td></tr><tr><td>Total liabilities</td><td>$-1,368.8</td><td>$-636.5</td></tr><tr><td>Deferred tax assets relating to:</td><td></td><td></td></tr><tr><td>Difference between book and tax basis of property</td><td>$206.8</td><td>$55.4</td></tr><tr><td>Accruals not currently deductible</td><td>504.1</td><td>140.9</td></tr><tr><td>Deferred taxes on FIN 48 state tax and interest impact</td><td>99.1</td><td>—</td></tr><tr><td>Net operating loss carryforwards, state taxes</td><td>157.8</td><td>27.5</td></tr><tr><td>Other credits and carryforwards</td><td>11.8</td><td>—</td></tr><tr><td>Capital loss carryforwards</td><td>18.6</td><td>—</td></tr><tr><td>Total assets</td><td>998.2</td><td>223.8</td></tr><tr><td>Valuation allowance</td><td>-156.4</td><td>-27.5</td></tr><tr><td>Net deferred tax asset</td><td>841.8</td><td>196.3</td></tr><tr><td>Net deferred tax assets (liabilities)</td><td>$-527.0</td><td>$-440.2</td></tr></table>
<table><tr><td></td><td>2008</td><td>2007</td><td>2006</td></tr><tr><td>Collection:</td><td></td><td></td><td></td></tr><tr><td>Residential</td><td>$966.0</td><td>$802.1</td><td>$758.3</td></tr><tr><td>Commercial</td><td>1,161.4</td><td>944.4</td><td>883.6</td></tr><tr><td>Industrial</td><td>711.4</td><td>645.6</td><td>654.1</td></tr><tr><td>Other</td><td>23.2</td><td>19.5</td><td>22.4</td></tr><tr><td>Total Collection</td><td>2,862.0</td><td>2,411.6</td><td>2,318.4</td></tr><tr><td>Transfer and disposal</td><td>1,343.4</td><td>1,192.5</td><td>1,182.1</td></tr><tr><td>Less: Intercompany</td><td>-683.5</td><td>-612.3</td><td>-588.6</td></tr><tr><td>Transfer and Disposal, Net</td><td>659.9</td><td>580.2</td><td>593.5</td></tr><tr><td>Other</td><td>163.2</td><td>184.4</td><td>158.7</td></tr><tr><td>Revenue</td><td>$3,685.1</td><td>$3,176.2</td><td>$3,070.6</td></tr></table>
<table><tr><td></td><td></td><td></td><td>Notional Amount</td><td></td></tr><tr><td></td><td></td><td></td><td>(in Gallons</td><td>Contract Price</td></tr><tr><td>Inception Date</td><td>Commencement Date</td><td>Termination Date</td><td>Per Month)</td><td>per Gallon</td></tr><tr><td>September 22, 2008</td><td>January 1, 2009</td><td>December 31, 2011</td><td>150,000</td><td>$4.1600-4.1700</td></tr><tr><td>March 17, 2008</td><td>January 5, 2009</td><td>December 31, 2012</td><td>50,000</td><td>3.7200</td></tr><tr><td>March 17, 2008</td><td>January 5, 2009</td><td>December 31, 2012</td><td>50,000</td><td>3.7400</td></tr><tr><td>November 5, 2007</td><td>January 5, 2009</td><td>December 30, 2013</td><td>60,000</td><td>3.2815</td></tr><tr><td>January 26, 2007</td><td>January 7, 2008</td><td>December 29, 2008</td><td>500,000</td><td>2.8285</td></tr><tr><td>January 26, 2007</td><td>January 5, 2009</td><td>December 28, 2009</td><td>500,000</td><td>2.8270</td></tr><tr><td>January 26, 2007</td><td>January 4, 2010</td><td>December 27, 2010</td><td>500,000</td><td>2.8100</td></tr><tr><td>August 29, 2006</td><td>October 2, 2006</td><td>December 31, 2007</td><td>500,000</td><td>3.1450</td></tr></table>
<table><tr><td></td><td>2012</td><td>2011</td><td>2010</td></tr><tr><td>Current:</td><td></td><td></td><td></td></tr><tr><td>Federal</td><td>$228.7</td><td>$201.7</td><td>$253.9</td></tr><tr><td>State</td><td>29.2</td><td>38.6</td><td>50.2</td></tr><tr><td>Federal and state deferred provision</td><td>83.9</td><td>334.8</td><td>61.4</td></tr><tr><td>Uncertain tax positions and interest, and other</td><td>-90.0</td><td>-257.7</td><td>4.0</td></tr><tr><td>Provision for income taxes</td><td>$251.8</td><td>$317.4</td><td>$369.5</td></tr></table>
<table><tr><td></td><td>2012</td><td>2011</td><td>2010</td></tr><tr><td>Balance at beginning of year</td><td>$48.1</td><td>$50.9</td><td>$55.2</td></tr><tr><td>Additions charged to expense</td><td>29.7</td><td>21.0</td><td>23.6</td></tr><tr><td>Accounts written-off</td><td>-32.5</td><td>-23.8</td><td>-27.9</td></tr><tr><td>Balance at end of year</td><td>$45.3</td><td>$48.1</td><td>$50.9</td></tr></table>

Question: what was the percentage change in the additions charged to expense from 2011 to 2012 as part of the allowance for doubtful accounts
Answer: 0.41429
Reasoning program: subtract(29.7,21.0), divide(#0,21.0)