Question

. After how many places of decimal, does the decimal expansion of (3/3125) terminates? (without actual division)​

Answer 1

Answer:

5 decimal places.

Step-by-step explanation:

In a rational no. p/q where q= 2^a x 5^b, the decimal expansion terminates after k places where k is the value greater among a and b .

So,

Prime factorisation of the denominator = 3125 = 5 x 5 x 5 x 5 x 5 = 5^5.

5^5 = 2^0 x 5^ 5 (as 2^0 = 1)

a = 0 and b= 5 ......5 is greater than 0

Hence the decimal expansion of 3/3125 will terminate after 5 decimal places.

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