Question

without actually performing long division state whether 543/225 has a terminating decimal expansion or non terminating decimal expansion

Answer 1

Answer:hey mate here is the ans as we know that non terminating decimal are those wich cannot be expressed in the form 2^m ×5^n and here is a non terminating decimal

Step-by-step explanation:

Answer 2

Answer:

It is an non-terminating decimal expansion. Because a terminating expansion is in which the denominator can be expressed as $2^{m} \times 5^{n}$.

Step-by-step explanation:

A number includes a terminating decimal expansion if the numbers behind the decimal point terminate or are finite.

Example:

The fraction 5/10 contains the decimal expansion of 0.5, which exists as a terminating decimal expansion because digits behind the decimal point stop behind one digit.

Non-terminating decimals expansion is the one that does not contain an end term. It contains an infinite number of terms.

Let, $&\frac{543}{225}$

$&\frac{225}{543}=5 \times 5 \times 3 \times 3$

$&\frac{525}{22}=\frac{54}{5^{2} * 3^{2}}$

This is non-terminating decimal expansion. Because a terminating expansion is in which the denominator can be expressed as $2^{m} \times 5^{n}$.

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