The number of places after which

17

320

terminates is ____.

Question

The number of places after which

17
    
     320

terminates is ____.

Accepted Answer

The number of places after which

17
    
     320

terminates is 6.We can rewrite the number as follows,

17
      
       320
     
     =
      
       17
      
       2×2×2×2×2×2×5

=
      
       17

2
        6
       
       ×5

So, we know that for any rational number in the standard form, i.e.,

p
    q

, where p and q are integers and q is non-zero, if q can be expressed as a product of its prime factors of the general form

(
    2
    x
   
   ×
    5
    y
   
   )
 , where x and y are positive integers, then the rational number is said to terminate.We can observe that the denominator is

(
    2
    6
   
   ×5)=(
    2
    x
   
   ×
    5
    y
   
   )
 , which means that the rational number will terminate. Now to make the denominator a power of 10, we will multiply the numerator and the denominator of the rational number by

5
    4

and simplify as follows,

17
      
       320
     
     =
      
       17×
        5
        4

2
        6
       
       ×5×
        5
        4

17
      
       320
     
     =
      
       17×625
      
       64×5×625

17
          
           320
         
         =
          
           10625
          
           1000000

17
          
           320
         
         =0.010625

So, the decimal expansion of the rational number is obtained as 0.010625 which terminates after 6 decimal places. Hence,

17
    
     320

terminates after 6 decimal places.

The number of places after which $17320$ terminates is ____.

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The number of places after which 17 320 terminates is ____.

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The number of places after which $17320$ terminates is ____.