Question

express 0.245( bar under 45)as a fraction in simplest form

Answer 1

Let x = 0.2454545....
100x = 24.555.... -(1)
1000x = 245.555....-(2)
Subtract (1) from (2)
1000x-100x=245.555....-24.555....
900x=221
x=221/900

0.2454545.. as a fraction in the simplest form is 221/900.

Answer 2

Answer:

The simplest form of the given number in p/q form is 27/110

Solution:

Given that

$0.2 \overline { 45 }$

Assume a fraction $\frac {p}{q}$ , where p is the numerator and q is the denominator.  

Therefore,

$\frac { \mathrm { p } } { \mathrm { q } } = 0.2454545 \ldots \ldots$

Multiply the number 10 on both sides, Now we get,

$\begin{array} { l } { 10 \times \frac { \mathrm { p } } { \mathrm { q } } = 10 \times 0.2454545 \ldots . } \\\\ { 10 \frac { \mathrm { p } } { \mathrm { q } } = 02.454545 \ldots . - ( 1 ) } \end{array}$

Multiply the number 1000 on both sides, we get

$\begin{array} { l } { 1000 \times \frac { \mathrm { p } } { \mathrm { q } } = 1000 \times 0.2454545 } \\\\ { 1000 \frac { \mathrm { p } } { \mathrm { q } } = 245.454545 \ldots \ldots ( 2 ) } \end{array}$

Subtract the equation (1) from (2)

We get,

$\begin{array} { l } { 1000 \frac { \mathrm { p } } { \mathrm { q } } = 245.454545 } \\\\ { 10 \frac { \mathrm { p } } { \mathrm { q } } = 2.454545 } \\\\ { 990 \frac { \mathrm { p } } { \mathrm { q } } = 243 } \end{array}$

$\begin{aligned} \frac { p } { q } & = \frac { 243 } { 990 } \\\\ \frac { p } { q } & = \frac { 81 } { 330 } \\\\ \frac { p } { q } & = \frac { 27 } { 110 } \end{aligned}$

Thus, the simplest form of the given number in p/q form is 27/110