Question

The decimal representation of 41/1250
will
(a) Terminate after 1 place
(b) Terminate after 4 places
(c) Terminate after 3 places
(d) Not Terminate​

Answer 1

Answer:

(C) terminate after 4 places

Step-by-step explanation:

1250 = 2^1 x 5^4

Answer 2

option (b)

The decimal representation of 41/1250  will Terminate after 4 places

Step-by-step explanation:

The decimal representation of 41/1250

let x = $\frac{p}{q}$ be a rtional number

such that the prime factorization of q is in the form of $2^n5^m$

where n,m are non negative integers .

then

decimal expansion of x is

= $\frac{41}{1250}$

= $\frac{41}{2\times5^4}$

multiplying and divide it by $2^3$

we get,

= $\frac{41\times2^3}{2\times5^4\times 2^3}$

= $\frac{328}{10000}$

= 0.0328

hence,

option (b)

The decimal representation of 41/1250  will Terminate after 4 places

#Learn more:

The decimal representation of 6/1250 will terminate after how many places of decimals

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