has the rational 441/22x55x72 have a terminating or non terminating decimal expansion?
Answers
Answer:
Since the denominator of this rational number is in the form of 2^ m * 5^n,so it will have terminating decimal representation.
The rational number 441/2²x5⁵x7² has a terminating decimal expansion.
Given:
The rational 441/2²x5⁵x7²
To find:
Is the rational have a terminating or non-terminating decimal expansion?
Solution:
The rational number 441/2²× 5⁵ × 7²
On simplifying the above fraction
=> 441 /(2²x5⁵x7²) = (3² × 7²)/(2² × 5⁵× 7²) = 3²/(2² × 5⁵)
To determine if the decimal expansion of this rational number is terminating or non-terminating, check the prime factorization of the denominator.
A rational number has a terminating decimal expansion if and only if its denominator can be expressed as a product of powers of 2 and 5.
In the above fraction, the denominator is (2² × 5⁵)
Therefore,
The rational number 441/2²x5⁵x7² has a terminating decimal expansion.
Learn more at
https://brainly.in/question/14397674
#SPJ6