Question

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after (a) one decimal place (b) two decimal place (c) three decimal place (d) four decimal place

Answer 1

SOLUTION:

Option (d) is Correct : four decimal place

Given : 14587/1250

14587/1250 = 14587/2¹ × 5⁴

14587/2¹ × 5⁴ = 14587 × 2³/2¹ × 5⁴ × 2³

14587/2¹ × 5⁴ = 14587 × 2³/2¹ × 5⁴ × 2³

= 14587 × 2³/2⁴ × 5⁴  

= 14587 × 2³/(2 × 5)⁴

= 14587 × 8 / 10⁴

= 116,696 / 10000

= 11.6696

The decimal expansion of 14587/1250 is 11.6696.

14587/1250 has terminating decimal expansion.  

Hence,The decimal expansion of  14587/1250 terminate after 4 places of decimal.

★★ If the factors of denominator of the given rational number is of form 2^m 5ⁿ ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.It terminates after k places of decimals where k is the larger of m and n.

HOPE THIS ANSWER  WILL HELP YOU...

Answer 2

Solution :

Given 14587/1250 is a terminating

decimal.

Since ,

Denominator ( q ) = 1250 is of the form

2ⁿ × 5^m .

q = 1250 = 5⁴ × 2¹

Now ,

14587/1250

= ( 14587 )/( 5⁴ × 2¹ )

= ( 14587 × 2³ )/( 5⁴ × 2⁴)

= ( 14587 × 8 )/( 10 )⁴

= 116696/10000

= 11.6696

Therefore ,

Option ( d ) is correct.

•••••