decimals to fractions (1 Viewer)

[Premus]

Hey

how do you convert 0.25313131...... into a fraction using the geometric series and limiting sum method?
Can you do it this way? or do you have to do it the algebraic way where u let x = 0.25313131.. and so on

Thanks!

 

[Supra]

im not sure thats ext 1, thats more 2u, i havent seen shit like this for ages but from memory
but yeh u need to know BOTH ways coz they can specify which way they want u to use in the 2u exam

x=0.25313131
100x=25.313131
99x=25.06
x=2506/9900

Geometric Method:

0.25313131=0.25+[0.0031+0.000031+...] the stuff in the brackets is a limiting sum

a/1- r

subbing in a=0.0031 and r= 0.01

0.0031
------
0.99

which is 31/9900

now add hte .25 to the 31/9900 and u get 2506/9900



at the end of both of these methods ensure u simplify the fractions to 1253/4950