Question

Without actual division ,find whether the rational number 1323/6*3***35*2has a terminating or a non terminating decimal

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The rational number 1323/6*3***35*2 has a terminating decimal without actual division.

Step-by-step explanation:

Given: The rational number 1323/6*3***35*2

To find: The given rational number is terminating or non terminating decimal expansion

Terminating decimal point:

• A rational number is terminating if it can be expressed in the form $\frac{p}{2^{n} . 5^{m} }$
• The rational number whose denominator is a number that has no other factor than 2 or 5, will terminate the result sooner or later after the decimal point.
• Then the decimal expansion of the number is terminating.

Let  $x = \frac{1323}{6^{3}. 35^{2} }$

    =  $\frac{1323}{6 . 6 .6.35.35}$

    = $\frac{1}{200}$

     =  $\frac{1}{2.2.2.5.5}$

      = $\frac{1}{2^{3 . 5^{2} } }$

Since the prime factorization of the denominator is of the form  of $2^{n} . 5^{m}$ where n and m are non negative integers.

Hence the number x has a terminating decimal expansion.

Final answer:

The rational number 1323/6*3***35*2 has a terminating decimal without actual division.

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