The decimal expansion of the rational number \(\frac{43}{2^4\times 5^

1.	The decimal expansion of the rational number \(\frac{43}{2^4\times 5^3}\) will terminate after how many places of decimals?
Answer» Let x = \(\frac{p}{q}\) be a rational number, such that the prime factorization of q is of the form 2ⁿ 5^m, where n, m are non - negative integers. Then 'x' has a decimal expansion which terminates after n or m places, whichever is maximum The maximum power of 2 or 5 in the given rational number is 4. So, it will terminate after 4 places of decimals. The decimal expansion of the given rational number will terminate after 4 places of decimals.

The decimal expansion of the rational number \(\frac{43}{2^4\times 5^3}\) will terminate after how many places of decimals?

Answer»

Let x = \(\frac{p}{q}\) be a rational number, such that the prime factorization of q is of the form 2ⁿ 5^m, where n, m are non - negative integers.

Then 'x' has a decimal expansion which terminates after n or m places, whichever is maximum

The maximum power of 2 or 5 in the given rational number is 4.

So, it will terminate after 4 places of decimals.

The decimal expansion of the given rational number will terminate after 4 places of decimals.