Question

The decimal expansion of the rational number 43/2⁴.5³ will terminate after how many of decimal

Answer 1

Answer:

the highest degree of the denominator is 4 then it will terminate after 4 places of decimal

Answer 2

Given:

A rational number 43/2⁴.5³.

To find:

After how many places of decimal, the decimal expansion of the rational number 43/2⁴.5³ will terminate.

Solution:

To answer this question, first of all, we should know that, a rational number which is in the p/q form is said to be a terminating rational number if its denominator consists of a number that can be written as the multiples of only 2, 5 or both.

Also,

in such cases, the number that has the highest multiples 'n' will terminate the rational number after n places of decimal.

So, as given, we have,

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

As it is in the multiples of 2 and 5 and 2 has the highest power i.e. 4 as compared to 5 which has 3 powers.

So, the given rational number will terminate after 4 places of decimal.

Hence, The decimal expansion of the rational number 43/2⁴.5³ will terminate after 4 places of decimal.