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The decimal representation $14587 21 × 54$ will terminate after how many decimal places?

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answer is C.

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Detailed Solution

Given expression is

14587 21 × 54

.
Let us multiply

23

in numerator and denominator. We get,

14587 21 × 54 × 2323

= 14587 21 × 54 × 2323

= 14587 × 23 21 × 23 × 54

= 14587 × 23 24 × 54

We know,

a m × b m = (a b) m

⇒ 14587 × 23 104

Now, we can observe that the denominator is

104

.
The power of 10 is 4.
Hence, the decimal representation of

14587 21 × 54

will terminate after four decimal places.
The correct option is (3).

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