Question

The decimal expansion of a rational number can never be _______

Answer 1

Answer:

Non - terminating, Non - repeating

Step-by-step explanation:

The decimal representation of a rational cannot be NON - terminating, NON - REPEATING because the decimal expansion of rational numbers is either terminating or non - terminating recurring

Answer 2

Given :  The decimal expansion of a rational number  can never be _________.​

To Find :  fill in the blank

Solution:

All real numbers can be divided in 2 categories

Rational numbers and irrational numbers

Rational number can be represented in the form of p/q

where p and q are integers and q≠ 0

if p and q are co prime

then if q  doe not have any prime factor other than 2 and 5 then

rational number is terminating decimal

1/2 is terminating decimal

if q has any prime factor other than 2 or 5 then

its non terminating recurring decimals

1/3 is non terminating repeating decimal

All real numbers which are not rational are irrational

irrational numbers are non terminating non recurring

√2 is  non terminating non recurring

Hence  The decimal expansion of a rational number  can never be non terminating non recurring .

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