Expressed 0-55- in the form p-q where p and q are integers and q - 0-

Let x = 0.55... Multiply 10 on both the sides we get, 10x = 10 × (0.55...) 10x nbsp; = 5.55... 10x nbsp;= 5 + 0.555... nbsp; 10x = 5 + x Solving for x, w ...

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

Byju's Answer

Standard IX

Mathematics

Types and Simplest Form of Surds

Expressed 0.5...

Question

Expressed 0.55.. in the form $\frac{p}{q}$ where p and q are integers and q ≠ 0.

Open in App

Solution

Let x = 0.55...
Multiply 10 on both the sides we get,
10x = 10 × (0.55...)
10x = 5.55...
10x = 5 + 0.555...
10x = 5 + x
Solving for x, we get

9x = 5, i.e., x = $\frac{5}{9}$
= $\frac{5}{9}$

Suggest Corrections

Similar questions

Q. Express

0.2 ¯ ¯¯¯¯ ¯ 52

in the form

\frac{p}{q}

where

p

and

q

are integers,

q \neq 0

Q. Express

1.3 ¯ ¯¯¯¯ ¯ 23

in the form

\frac{p}{q}

where

p

and

q

are integers,

q \neq 0

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

Q. Express

0.4 ¯ 7

in the form

\frac{p}{q}

, where p and q are integers and

q \neq 0

Q. Express

0. ¯ ¯¯¯¯¯¯ ¯ 975

in the form of

\frac{p}{q}

, where

p

and

q

are integers and

q \neq 0

Join BYJU'S Learning Program

Expressed 0.55.. in the form pq where p and q are integers and q ≠ 0.

Let x = 0.55... Multiply 10 on both the sides we get, 10x = 10 × (0.55...) 10x = 5.55... 10x = 5 + 0.555... 10x = 5 + x Solving for x, we get 9x = 5, i.e., x = 59 = 59

Expressed 0.55.. in the form $\frac{p}{q}$ where p and q are integers and q ≠ 0.

Let x = 0.55...
Multiply 10 on both the sides we get,
10x = 10 × (0.55...)
10x = 5.55...
10x = 5 + 0.555...
10x = 5 + x
Solving for x, we get

9x = 5, i.e., x = $\frac{5}{9}$
= $\frac{5}{9}$