Question

the decimal expansion of the rational number 14587/1250 will terminate after how many 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

$=\frac{14587}{2 \times 5^{4}}$

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

$\begin{array}{l}{=\frac{14587 \times 2^{3}}{2^{4} \times 5^{4}}} \\ {=\frac{14587 \times 8}{(2 \times 5)^{4}}}\end{array}$

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:

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