MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Irrational Numbers

D is a real n...

Question

D is a real number which noon terminating digits a1 and a2 after the decimal point. Let D= 0.a1 a2 a1 a2........with a1 and a2 both not zero which of the following when mutiplied by D will necessarily give an integer?

Options:

18

198

125

75

Open in App

Solution

Option B

D=0.a1 a2 a1 a2....= 0.a1 a2 (1+0.01+0.01^2+....+0.01^n+.....)

D= 0.a1 a2 (1/(1-0.01))=0.a1 a2 /0.99=(a1 a2)/99

so, integer should be k99. therefore, B 198=299
Hope you understood

Your teacher

Suggest Corrections

thumbs-up

3

Similar questions

D

is a real number with non terminating digits

a_{1}

a_{2}

after the decimal point. Let

D = 0, a_{1} a_{2} a_{1} a_{2} . . . . . . . .

a_{1} & a_{2}

both not zero which of the following when multiplied by

D

will necessarily give an integer ?

Q. Let D be a recurring decimal of the form

D = 0. a_{1} a_{2} a_{1} a_{2} a_{1} a_{2} . . . . . . . . . . . .;

a_{1}

a_{2}

lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D? (CAT 2000)

Q. L Let D be a recurring decimal of the form

D = 0. a_{1} a_{2} a_{1} a_{2} a_{1} a_{2} . . . . . . . . . . . .;

a_{1}

a_{2}

lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D? (CAT 2000)

Q. Let D be a recurring decimal of the form

D = 0. a_{1} a_{2} a_{1} a_{2} a_{1} a_{2} . . . .,

_{1}

_{2}

0

9

. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D?

A_{1}

A_{2}

are two matrices of order 3

\times

3 satisfying the matrix equations

3 A_{1}^{T} + I^{3} = 10 A_{1}

4 I^{3} + 3 A_{2} = 7 A_{2}^{T}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction to Number Systems

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Irrational Numbers

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon