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The decimal expansions of $13125$ is ____.

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Detailed Solution

The decimal expansions of

13125

is 0.104.
Given a number

13125

.
Factors of the denominator are,

13125 = 13 20 ​ ​ × ​ ​ 5 ​ ​ 3 ​ ​ ​ ​ ​ ​

Multiplying and dividing by 2³,

⇒ 13 ​ ​ × ​ ​ 2 ​ ​ 3 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ 20 ​ ​ × ​ ​ 5 ​ ​ 3 ​ ​ ​ ​ × ​ ​ 2 ​ ​ 3 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​

⇒ 13 ​ ​ × ​ ​ 2 ​ ​ 3 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ 1 ​ ​ × ​ ​ 5 ​ ​ 3 ​ ​ ​ ​ × ​ ​ 2 ​ ​ 3 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​

⇒ 13 ​ ​ × ​ ​ 8 ​ ​ ​ ​ ​ ​ ​ ​ 1 ​ ​ × ​ ​ 5 ​ ​ 3 ​ ​ ​ ​ × ​ ​ 2 ​ ​ 3 ​ ​ ​ ​ ​ ​

⇒ 104 2 ​ ​ × ​ ​ 5 ​ ​ 3 ​ ​

⇒ 104 10 ​ ​ 3 ​ ​

⇒ 1041000

⇒ 0.104

Hence, the decimal expansion is 0.104.

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