Question

Look at several examples of rational numbers in the form $straight p over straight q left parenthesis q not equal to 0 right parenthesis comma$ where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

Examples

left parenthesis straight i right parenthesis space 1 half equals fraction numerator 1 cross times 5 over denominator 2 cross times 5 end fraction equals 5 over 10 equals 0.5 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left enclose space straight q equals 2 end enclose left parenthesis ii right parenthesis space 1 fourth equals fraction numerator 1 cross times 25 over denominator 4 cross times 25 end fraction equals 25 over 100 equals 0.25 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left enclose space straight q equals 2 end enclose squared left parenthesis iii right parenthesis space 3 over 8 equals fraction numerator 1 cross times 125 over denominator 8 cross times 125 end fraction equals 375 over 1000 equals 0.375 space space space space space space space space space space space space space space space space space space space space space space space space space left enclose space straight q equals 2 end enclose cubed left parenthesis iv right parenthesis space 31 over 25 equals fraction numerator 31 cross times 4 over denominator 25 cross times 4 end fraction equals 124 over 100 equals 1.24 space space space space space space space space space space space space space space space space space space space space space space space space space space space space left enclose space straight q equals 5 squared end enclose left parenthesis straight v right parenthesis space 7 over 125 equals fraction numerator 7 cross times 8 over denominator 125 cross times 8 end fraction equals 56 over 1000 equals 0.056 space space space space space space space space space space space space space space space space space space space space space space left enclose space straight q equals 5 cubed end enclose left parenthesis vi right parenthesis space 13 over 20 equals fraction numerator 13 cross times 5 over denominator 20 cross times 5 end fraction equals 65 over 100 equals 0.65 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left enclose space straight q equals 2 end enclose squared cross times 5 left parenthesis vii right parenthesis space 29 over 16 equals fraction numerator 29 cross times 625 over denominator 16 cross times 625 end fraction equals 18125 over 10000 equals 1.8125 space space space space space space space space space space space space space space space space space left enclose space straight q equals 2 end enclose to the power of 4

The property that q must satisfy is that the prime factorisation of q must have only powers of 2 or powers of 5 or both.

For Daily Free Study Material Join wiredfaculty

Polynomials

Some More Questions From Polynomials Chapter

Find two rational numbers between 0.1 and 0.2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction