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What is \(0.4\overline8 + 0.\overline{37}\)? Express your answer as a common fraction in lowest terms.

 Jan 11, 2021
 #1
avatar+114361 
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Fractional representation  of a repeating  decimal   =

 

[ number written without the decimal  - non-repeating part  ]

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[ same  no. of  9s  as digits in repeating part   same number of  0s as digits in non-repeating part ]  

 

 

 

Fractional representation of first repeating decimal      =     [  48 - 4 ]   /  90  =  44/90 =  22/45

 

Fractional representation of second decimal  =   [ 37   - 0 ] / 99   = 37/99

 

So ....   22/45  +  37/99  =     [  22 * 99   +   37*45  ]  /  [ 45 * 99  ]   =  427/495

 

 

cool cool cool

 Jan 11, 2021

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