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The denominator of the rational number $2575000$ in the form $2 m × 5 n,$ where m and n are non-negative integers is and its decimal expansion without actual division is .

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Detailed Solution

Given rational number is,

2575000

The denominator of

2575000

is 5000.
Let’s obtain the prime factorization of 5000.
So,

⇒ 5000 = 2 × 2500 ⇒ 5000 = 2 × 2 × 1250 ⇒ 5000 = 2 × 2 × 2 × 625 ⇒ 5000 = 23 × 54

Here, the denominator is of the form

2 m × 5 n

Also,

⇒ 2575000 ⇒ 2575000 × 22 ⇒ 51410000 ⇒ 0.0514

Therefore, the decimal expansion is 0.0514.
The denominator is of the form

23 × 54

and decimal expansion is 0.0514.

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