Question

What is 0.(24) ̅ (the 24 is repeating) expressed as a fraction in simplest form?

Answer 1

Hi,
a)let 0.24 be x.
100x(two zeros because two decimals are repeating)=24.24 ̅(24 is repeating)
Now subtract 100x-x on both sides. This forms an equation.
100x-x=24.24(.24 is repeating) -0.24(.24 is repeating)
99x=24
x=24/99
simplest form=8/33
b)Follow the same rule.
let 0.24(4 is repeating) be x
Since there is two decimals in total , 100x=24.44(4 is repeating)
But since there is one decimal that is repeating, there will be one zero. Hence  it will become 100x-10x= 24.4(4 is repeating)-2.4(4 is repeating and get the decimal point closest to the repeating decimal)
90x=22
x=22/90
Simplest form=11/45
c) 0.24 is expressed as 8/25
0.24/1
24/100(make it a whole number and add no. of zeros based on how many decimals places you move.)
Simplest form=6/25
Hope this helps you.