Question 12
The decimal expansion of the rational number 14587/1250 will terminate after:
one decimal place (b) two decimal places
(c) three decimal places (d) four decimal places
𝟏𝟒𝟓𝟖𝟕/𝟏𝟐𝟓𝟎
= 14587/(2^1 × 5^4 )
= 14587/(2^1 × 5^4 ) × 2^3/2^3
= (14587 × 2^3)/((2^4 × 5^4))
= (14587 × 2^3)/(2 × 5)^4
= (14587 × 2^3)/〖10〗^4
So, the number will terminate after 4 decimal places
So, the correct answer is (D)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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