Question

check whether 53 by 300 will terminate or non terminate​

Answer 1

$\huge \rm{Question}$

$\rm \pink{check \: whether \: \frac{53}{300} \: will \: terminate \: or \: non \: terminate}$

$\LARGE \rm{ \frac{53}{300}}$

( We will find the prime factorization of the denominator.)

$\sf \red{prime \: factorisation \: of \: 300 = 2 \times 2 \times 3 \times 5}$

$\\ \therefore \sf{ \frac{53}{300} \: will \: have \: non - terminating \: representatives}$

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☁️ Remember !!

☞2 and 5 all the prime factors of all denominators. Therefore, if we have only 2 and 5 as the prime factors of the denominator of a rational number in the lowest term, it will have terminating decimal representation. But, if the prime factors of the denominators are also other than 2 and 5, the decimal representation of that rational number (in the lowest term) will be are non- terminating repeating decimal.

Additional information

• Every rational number can be represented as a decimal.

• The decimal representation of a rational number is either terminating or non terminating but repeating.

• Decimal numbers having a finite number of decimal places are known as terminating decimal number.

• Decimal numbers having an infinite number of a decimal places are known as non terminating decimal numbers.

• If the denominator of a rational number in the standard form has 2 or 5 or both as the only prime factors then it can be represented as a terminating decimal.

• If the denominator of a rational number in the standard form has prime factors other than 2 and 5, then it cannot be represented as a terminating decimal. In fact, it is a non terminating but repeating decimal.

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Answer 2

Lets understand about the concept first .

Concept :

Whenever we divide any number by any if we can find the answer then its terminating rational number but if the Quotient of number is repeating again its non terminating number.

Now lets come to the question ,

Question is asked that we have to check wheter 53/300 will terminate or not .

which is ,

$\frac{53}{300}$

For finding that we always need to remove prime factors of the denomintor i.e 300.

Prime factors of 300 = 2×2 ×3×5

For more info ,

53 is prime factor of its own number .

By analysing it , we can understand that 53/100 is a non terminating rational number.

$∴ \: \frac{53}{300}$ is non terminating rational numbers or representatives too.[tex][/tex]