Question

After how many decimal places,will the decimal expansion of the rational number 325/2^4 5^3 terminate

Answer 1

the answer would be 0.1625

Answer 2

Answer:

The given rational number will terminate after 4 places - 0.1625

Step-by-step explanation:

Given : Rational number $\frac{325}{2^4\times 5^3}$

To find : After how many decimal places,will the decimal expansion of the rational number given terminate?

Solution :

If the denominator of a rational number is of the form$2^n5^m$ , then it will terminate after n places if n>m or m places if m>n.

The given rational number is

$\frac{325}{2^4\times 5^3}$

Here, n = 4 > 3 = m , n>m

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

Check by solving,

$=\frac{325}{2^4\times 5^3}$

$=\frac{325\times 5}{2^4\times 5^3\times 5}$

$=\frac{1625}{(2\times5 )^4}$

$=\frac{1625}{(10^4}$

$=\frac{1625}{(10000}$

$=0.1625}$