Question

write the decimal form of the rational number 7/2^2×5 ​

Answer 1

Step-by-step explanation:

7/2^2 x5

49/4x5

245/4

61.25

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Answer 2

The decimal form of the rational number 7/(2² × 5) is 0.35.

Given rational number:  7/(2² × 5) ​

To find : The decimal form of a given rational number.

Concept used :

"If the factors of the denominator of the given rational number are of form 2^m 5ⁿ, where n and m are non-negative integers, then the decimal expansion of the rational number is terminating otherwise non-terminating recurring."

Here, the factors of the denominator are 2² × 5¹, which is in the form 2^m 5ⁿ. So, 7/(2² × 5) has a terminating decimal expansion.

Solution :

Step 1: Simply by multiplying and dividing the given rational number by 5¹.

7/(2² × 5¹)  = (7 × 5¹) / (2² × 5¹ × 5¹)

Step 2 : Simplify the numerator and denominator:

7/(2² × 5)  = (7 × 5) / (2² × 5²)

7/(2² × 5) = (7 × 5) / (2 × 5)²

7/(2² × 5) = 35 / 10²

7/(2² × 5) = 35 /100

7/(2² × 5) = 0.35  

Hence, the decimal form of 7/(2² × 5) is 0.35.

Correct question :

Write the decimal form of the rational number 7/(2^2×5 ​).

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