Log in to add a comment

## Answers

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

5.4178 bar is the rational number with the last four digits repeating infinitely.

5.4178 4178 4178 4178 ....

Simple rule to write in the rational number form is : 4178 is four digits. so take 0.0001. here 1 is in the 4 th decimal place. subtract it from 1 and get q. the numerator p = 0.4178, the given repeating number without bar on top.

p / q = 5.0 + [ 0.4178 / (1 - 0.0001) ] = 5.4173 / 0.9999

= 54173 / 9999

This can be obtained by using geometric progression formula too.

5.0 + 0.4178 + 0.00004178 + 0.0000 0000 4178 + ...

= 5.0 + 0.4178 [ 1 + 0.0001 + 0.0000 0001 + .. ]

= 5.0 + 0.4178 * 1 / [ 1 - 0.0001 ]

= 5.0 + 0.4178 / 0.9999 = 5.4173 / 0.9999 = 54173 / 9999

5.4178 4178 4178 4178 ....

Simple rule to write in the rational number form is : 4178 is four digits. so take 0.0001. here 1 is in the 4 th decimal place. subtract it from 1 and get q. the numerator p = 0.4178, the given repeating number without bar on top.

p / q = 5.0 + [ 0.4178 / (1 - 0.0001) ] = 5.4173 / 0.9999

= 54173 / 9999

This can be obtained by using geometric progression formula too.

5.0 + 0.4178 + 0.00004178 + 0.0000 0000 4178 + ...

= 5.0 + 0.4178 [ 1 + 0.0001 + 0.0000 0001 + .. ]

= 5.0 + 0.4178 * 1 / [ 1 - 0.0001 ]

= 5.0 + 0.4178 / 0.9999 = 5.4173 / 0.9999 = 54173 / 9999