republic services , inc . notes to consolidated financial statements 2014 ( 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% ( 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 the following table reflects the activity in our allowance for doubtful accounts for the years ended december 31 , 2012 , 2011 and 2010: .

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 | 2012 | 2011 | 2010
----------|----------|----------|----------
balance at beginning of year | $ 48.1 | $ 50.9 | $ 55.2
additions charged to expense | 29.7 | 21.0 | 23.6
accounts written-off | -32.5 ( 32.5 ) | -23.8 ( 23.8 ) | -27.9 ( 27.9 )
balance at end of year | $ 45.3 | $ 48.1 | $ 50.9
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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 post- closure 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. .

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