recurring decimals (1 Viewer)

[x1]

hi

stuck on this question.

2.8 (8 repeater)

write as a fraction.

 

[Squar3root]

spam your calculator and you get 26/9

 

[obliviousninja]

Lol

 

[x1]

ik that but how do u do it the fraction way?

like for 0.444444...
u do 4/10 + 4/100 + 4/1000 +...
then a=4/10 r=1/10

and then use sum to infinity equation.

 

[enigma_1]

2.8888888

= 2+ (0.8+0.08+0.008+………)

R=0.1 a=0.8

:. = 2+ a/(1-r) = 2+ 0.8/(1-0.1) = 2+8/9 = 26/9

 

[astroman]

 

[screwuhsc]

yea as astro mentioned u can do it 2 ways series and sequences method or the old fashioned old way

 

[Feynman]

let x = 2.8 repeater
10x = 28.8 repeater
subtract x from both sides
9x = 26
x = 26/9

 

[braintic]

yea as astro mentioned u can do it 2 ways series and sequences method or the old fashioned old way

The algebraic way is actually the way the Sum of GP formula is derived.