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$171800$ will terminate after ____ places.

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Detailed Solution

171800

terminates after 5 decimal places.
We can rewrite the number as follows,

171800 = 171 2 × 2 × 2 × 2 × 2 × 5 × 5 = 171 25 × 52

So, we can observe that the denominator is

(25 × 52) = (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

53

and simplify as follows,

171800 = 171 × 53 25 × 55 171800 = 171 × 125 32 × 3125 171800 = 21375100000 171800 = 0.21375

So, the decimal expansion of the rational number is obtained as 0.21375 which terminates after 5 decimal places.

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