Question

find decimal expansion of 51/750​

Answer 1

Answer:

0.072

Step-by-step explanation:

Answer 2

Answer:

Decimal expansion of $\frac{51}{750}$ is 0.068

Step-by-step explanation:

Explanation:

Given , $\frac{51}{750}$

Now we break the given value in small numbers

So, 51 can be written as $3^{1} 17^{1}$

and 750 = $2^{1}$×$3^{1}$×$5^{3}$

Therefore ,$\frac{51}{750} = \frac{(3^{1} ).(17^{1})}{2^{1}3^{1} 5^{3} }$  = $\frac{17}{2^{1} 5^{3} }$

Now , as we know that if the factors of denominator of the given rational number is of form $2^{n}5^{m}$ where n and m are non negative integers , then the decimal expansion of the rational number is terminating .

Step1:

$\frac{51}{750} = \frac{(17)}{2^{1} 5^{3} }$

⇒$\frac{51}{750} = \frac{(17)(4)}{2^{3} 5^{3} }$         (multiply denominator and numerator by $2^{2}$ )

⇒$\frac{51}{750} = \frac{(68)}{(2.5)^{3} }$

⇒$\frac{51}{750} = \frac{(68)}{(10)^{3} }$ = $\frac{68}{1000} = 0.068$

Final answer :

Hence , 0.068 is the decimal expansion of $\frac{51}{750}$ .