Solution To Moderate Exercise Number Two

MODERATE EXERCISES

(2) Convert 6.4__
(2) Convert 6.473 to rational form.

SOLUTION:

Let x = 6.4__
Let x = 6.473, so that x = 6.473737373... .

Note that 100x = 647.373737373... ,

so then 100x - x = - ( 647.373737373... )
so then 100x - x = - ( 646.473737373... )

so then 100x - x = - ( 640.900000000...

so then 100x - x = - ( ⁶⁴⁰⁹/₁₀

But 100x - x = 99x, so 99x = ⁶⁴⁰⁹/₁₀ implies

( ¹/₉₉ )( 99x ) = x = ( ¹/₉₉ )( ⁶⁴⁰⁹/₁₀ )

( ¹/₉₉ )( 99x ) = x = ⁶⁴⁰⁹/₉₉₀ .

Thus, 6.4__
Thus, 6.473 can be written in the rational form ⁶⁴⁰⁹/₉₉₀.

Click Here To Return To The Moderate Exercises.

Click Here To Return To The Main Menu.