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

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Detailed Solution

The number of places after which

17320

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

17320 = 17 2 × 2 × 2 × 2 × 2 × 2 × 5 = 17 26 × 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

(26 × 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

54

and simplify as follows,

17320 = 17 × 54 26 × 5 × 54 17320 = 17 × 625 64 × 5 × 625 17320 = 106251000000 17320 = 0.010625

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

17320

terminates after 6 decimal places.

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