{"pre_text": ["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: ."], "post_text": ["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. ."], "table": [["", "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"]], "table_ori": [["", "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)", "(23.8)", "(27.9)"], ["Balance at end of year", "$45.3", "$48.1", "$50.9"]]}

Question: what was the percentage change in the additions charged to expense from 2011 to 2012 as part of the allowance for doubtful accounts
Evidence:
table_2: the additions charged to expense of 2012 is 29.7 ; the additions charged to expense of 2011 is 21.0 ; the additions charged to expense of 2010 is 23.6 ;
Program: subtract(29.7, 21.0), divide(#0, 21.0)
Answer:
str_answer: 41.4%
exe_answer: 0.41429