Let x=21/1120 be a rational number then x has decimal expansion which terminates
Answers
Given : A rational number x = 21 /1120
To find : Whether x has a decimal expression which terminates
Solution:
x = 21 /1120
Lets first write it in simplest fraction form
=> x = 3 * 7 / ( 7 * 160)
Lets divide numerator & denominator by 7
=> x = 3/160
Simplest form is 3/160
Now any rational number has decimal expression which terminates if it has only 2 & 5 as prime factors in Denominator
Lets check 160
160 = 2 * 2 * 2 * 2 * 2 * 5
160 = 2⁵ * 5
= 160 = 10 * 2⁴
as only factor are 2 & 5
Hence number has decimal Expression which terminates
3/160
= 3/ 10 * 2⁴
= 3 * 5⁴ / 10 * 2⁴ * 5⁴
= 3 * 625 / 10⁵
= 1875/10⁵
= 0.01875
x = 21/1120 = 0.01875
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Step-by-step explanation: