Question

the decimal expansion of 43/162:
a) isterminating
b)is non terminating and non recurring
c) is non terminating and recurring
d) does not exist

Answer 1

The decimal expansion of 43/162  is non terminating and recurring

Rational numbers:

• Rational numbers are real numbers which can be written in the form p/q   where p and q are integers and q≠0
• All real numbers which are not rational  are irrationals.

• Any Rational number in the form of p/q  where p and q are co primes.
• if q has only prime factors of 2 and 5 then it is terminating decimal.
• if q has prime factors other than 2 and 5 also then its non terminating recurring decimal
• Rational numbers are terminating decimals or non terminating recurring decimal.
• Irrational numbers are non terminating non-recurring decimals

Given number is 43/162  comparing with p/q form

p = 43

q = 162

Prime Factorize q

q = 162 = 2 x 3 x 3 x 3 x 3 = 2 x 3⁴

As q (162) has prime factor 3  other than 2 and 5 so its non terminating recurring decimal

The decimal expansion of 43/162  is non terminating and recurring

Correct option is c)  non terminating and recurring

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Answer 2

Answer:

The correct answer is b) non terminating non recurring