The decimal expansion of the rational no. $\frac{43}{2^{4} . 5^{3}}$ will terminate after how many decimals?

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0.0215

2.15

0.215

1.0215

answer is A.

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Detailed Solution

Concept- Here, we'll identify the corresponding fraction, simplify the given fraction, and then calculate the needed number.
Consider the following expression:

\frac{43}{2^{4} . 5^{3}}

You can rewrite it as - =

\frac{43}{2^{4} \times 5^{3}}

Divide and multiply the expression. The final value does not change when you multiply or divide a word with the same value.
=

\frac{43 \times 5}{2^{4} \times 5^{3}} \times \frac{1}{5}

When there is a common base and a multiplicative sign in between, powers are added according to the law of power and exponent.
=

\frac{43 \times 5}{2^{4} \times 5^{3 + 1}}

Simplify =

\frac{43 \times 5}{2^{4} \times 5^{4}}

in the expression above.
When powers are equal, bases are multiplied, adhering once more to the law of powers and exponents.
=

\frac{43}{{(2 \times 5)}^{4}}

Simplify =435 in the previous expression (10)
4
Reduce the complexity of the expression - =

\frac{215}{1000}

.Decimalize the aforementioned fraction.
=0.0215
The specified rational number will therefore be rounded to the nearest four decimal digits.
Hence, option 1 is the best response.

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