Question

write the denominator of the rational no.377/4000 in the form 2^m5^n where m,n are non negative integers .hence write it's decimal expansion without actual division​

Answer 1

Answer:

Denominator of the rational number 257/ 5000 is 5000.

Now, 5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5

Now, 5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 = (2)^ 3 × (5)^ 4 , which is of the type 2m × 5n ,

(where m = 3 and n = 4 are non-negative integers.)

∴ Rational number = 257/5000

= 257/2^3×5^4 × 2/2

= 257/2^3×5^4 × 2/2 = 514/2^3×5^4

= 257/2^3×5^4 × 2/2 = 514/2^3×5^4 = 514/(10)^4

= 257/2^3×5^4 × 2/2 = 514/2^3×5^4 = 514/(10)^4 = 514/10000

= 257/2^3×5^4 × 2/2 = 514/2^3×5^4 = 514/(10)^4 = 514/10000 = 0.0514

So, 0.0514 is the required decimal expansion of the rational 257/5000 and it is also a terminating decimal number.

Step-by-step explanation:

$<marquee >$

✌Mark As Brainliest✌

Answer 2

Answer:

377 = 13 × 29

4000 = 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5

=> 377/ 4000 in form 2^n × 5^m = 377/2⁵ × 5³

=> decimal expansion of 377/4000 = 377 × 5²/2⁵ × 5³ × 5²

= 377 × 25/2⁵ × 5⁵ = 9425/10⁵ = 9425/100000 = 0.09424