Question 3 iii Express 0 - 001 in the form p - q- where p and q are integers and q-0-

Name: NCERT - Grade 09 - Mathematics - Number Systems - Q10_3
Uploaded: 2022-07-04T10:36:42+05:30
Description: 0.001= 0.001001... Let nbsp;x nbsp;= 0.001001... ⇒ 1000x nbsp;= 1.001001… nbsp;[Since, there are three repeating decimal digits, so multiply x with 100 ...

0.001= 0.001001... Let nbsp;x nbsp;= 0.001001... ⇒ 1000x nbsp;= 1.001001… nbsp;[Since, there are three repeating decimal digits, so multiply x with 100 ...

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

Byju's Answer

Standard X

Mathematics

Check If a Given Rational No. Is Terminating or Not

Question 3 ii...

Question

Question 3 (iii)
Express $0. ¯ ¯¯¯¯¯¯ ¯ 001$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Open in App

Solution

$0. ¯ ¯¯¯¯¯¯ ¯ 001$ = 0.001001...
Let x = 0.001001...
$\Rightarrow$ 1000x = 1.001001… [Since, there are three repeating decimal digits, so multiply x with 1000.]
$\Rightarrow$ 1000x = 1+ 0.001001
$\Rightarrow$ 1000x = 1 + x
$\Rightarrow$ 999x = 1
$\Rightarrow x = \frac{1}{999}$

Suggest Corrections

Similar questions

Question 3 (iii)
Express $0. ¯ ¯¯¯¯¯¯ ¯ 001$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Express $0. ¯ ¯¯¯¯¯¯ ¯ 001$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Question 3 (ii)
Express $0.4 ¯ 7$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Question 3 (i)
Express $0. ¯ 6$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

Q. Express the following in the form

\frac{p}{q}

, wher

p

and

q

are integers and

q \neq 0.

(i)

0. ¯ 6

(ii)

0.4 ¯ 7

(iii)

0. ¯ ¯¯¯¯¯¯ ¯ 001

Join BYJU'S Learning Program

Explore more

Check If a Given Rational No. Is Terminating or Not

Standard X Mathematics

Join BYJU'S Learning Program

Question 3 (iii) Express 0.¯¯¯¯¯¯¯¯001 in the form pq, where p and q are integers and q≠0.

0.¯¯¯¯¯¯¯¯001= 0.001001... Let x = 0.001001... ⇒ 1000x = 1.001001… [Since, there are three repeating decimal digits, so multiply x with 1000.] ⇒ 1000x = 1+ 0.001001 ⇒ 1000x = 1 + x ⇒ 999x = 1 ⇒x=1999

Question 3 (iii)
Express $0. ¯ ¯¯¯¯¯¯ ¯ 001$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$ .

$0. ¯ ¯¯¯¯¯¯ ¯ 001$ = 0.001001...
Let x = 0.001001...
$\Rightarrow$ 1000x = 1.001001… [Since, there are three repeating decimal digits, so multiply x with 1000.]
$\Rightarrow$ 1000x = 1+ 0.001001
$\Rightarrow$ 1000x = 1 + x
$\Rightarrow$ 999x = 1
$\Rightarrow x = \frac{1}{999}$