Question

03.
3. The decimal expansion of the rational number was will terminate after
(a) One decimal place
(b) Two decimal places
(c) Three decimal places
(d) Four decimal places.​

Answer 1

Answer:

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

Step-by-step explanation:

Given: 14587/1250

=\frac{14587}{2 \times 5^{4}}=2×5414587

Add 2^{3}23 to both numerator and denominator

\begin{gathered}\begin{array}{l}{=\frac{14587 \times 2^{3}}{2^{4} \times 5^{4}}} \\ {=\frac{14587 \times 8}{(2 \times 5)^{4}}}\end{array}\end{gathered}=24×5414587×23=(2×5)414587×8

Now simplify the above step by simple mathematical calculations

= 116696/10000

=11.6696

Hence here in the given problem the decimal places will terminate after 4 decimal places or decimal fractions.

So from this we can conclude that the rational numbers can be expressed in the form of decimal fractions also.

Answer 2

Answer:

(D) Four decimal places