Question

Write the decimal form of rational number 7/(2square×5)

Answer 1

Answer:

7/2square multiple by 5

Step-by-step explanation:

7/4×5

7/20

0.35

Answer 2

The decimal form of the rational number $\frac{7}{(2^2\times5)}$ is 0.35.

Given rational number:  $\frac{7}{(2^2\times5)}$

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 the form $2^m 5^n$, where n and m are non-negative integers, then the decimal expansion of the rational number is terminating otherwise non-terminating recurring."
• Here, in this question, the factors of the denominator are 2² × 5¹, which is in the form $2^m 5^n$. So, $\frac{7}{(2^2\times5)}$ has a terminating decimal expansion.

Solution :

Step 1 of 2: Simply by multiplying and dividing the given rational number by 5¹.

$\frac{7}{(2^2\times5)} =\frac{7\times5^1}{(2^2\times5^1\times5^1)}$

Step 2 of 2: Simplify the numerator and denominator:

$= \frac{7\times5^1}{(2^2\times5^2)}$

$= \frac{7\times5}{(2\times5)^2}$

$= \frac{35}{(10)^2}$

$= \frac{35}{100}$

$\frac{7}{(2^2\times5)}$ = 0.35  

Hence, the decimal form of $\frac{7}{(2^2\times5)}$ is 0.35.

Correct question :

Write the decimal form of the rational number $\frac{7}{(2^2\times5)}$.

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